messages
listlengths 2
2
| add_generation_prompt
bool 1
class | data
dict |
|---|---|---|
[
{
"content": "In his garden, Grandpa had counted 36 small tomatoes before going on vacation. When he came back from vacation, he counted 100 times more tomatoes. How many tomatoes grew in his absence?",
"role": "user"
},
{
"content": "I need to find how many tomatoes grew while Grandpa was on vacation.\n\nGiven information:\n- Before vacation: 36 small tomatoes\n- After vacation: 100 times more tomatoes than before\n\nFirst, let me calculate how many tomatoes there were after vacation:\n100 times more than 36 = 100 × 36 = 3,600 tomatoes\n\nNow I can find how many tomatoes grew during his absence:\nTomatoes that grew = Total after vacation - Total before vacation\nTomatoes that grew = 3,600 - 36 = 3,564 tomatoes\n\nTherefore, 3,564 tomatoes grew in Grandpa's absence.",
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] | true
|
{
"correct_answer": "Before going on vacation, Grandpa counts 36 tomatoes. After going on vacation, Grandpa has 100 * 36 = 3600 tomatoes. So in his absence, 3600 - 36 = 3564 tomatoes have grown. #### 3564",
"incorrect_answer": "Before going on vacation, Grandpa counts 36 tomatoes. After going on vacation, he counted 100 times more tomatoes, so he has 36 + 100 = 136 tomatoes. So in his absence, 136 - 36 = 100 tomatoes have grown. #### 100",
"messages": [
{
"content": "In his garden, Grandpa had counted 36 small tomatoes before going on vacation. When he came back from vacation, he counted 100 times more tomatoes. How many tomatoes grew in his absence?",
"role": "user"
},
{
"content": "Before going on vacation, Grandpa counts 36 tomatoes.\nAfter going on vacation, Grandpa has 100 * 36 = <<100*36=3600>>3600 tomatoes.\nSo in his absence, 3600 - 36 = <<3600-36=3564>>3564 tomatoes have grown.\n#### 3564",
"role": "assistant"
}
],
"short_incorrect_solution": "100",
"short_solution": "3564"
}
|
[
{
"content": "Tom's rabbit can run at 25 miles per hour. His cat can run 20 miles per hour. The cat gets a 15-minute head start. In hours, how long will it take for the rabbit to catch up?",
"role": "user"
},
{
"content": "I need to find when the rabbit catches up to the cat.\n\nLet me set up the problem:\n- Rabbit speed: 25 mph\n- Cat speed: 20 mph\n- Cat gets a 15-minute head start = 0.25 hours\n\nLet t = time (in hours) that the rabbit runs\n\nWhen the rabbit catches up, both animals will have traveled the same distance from the starting point.\n\nDistance traveled by rabbit = 25t\n\nDistance traveled by cat = 20(t + 0.25)\n(The cat runs for t hours plus the 0.25 hour head start)\n\nSetting the distances equal:\n25t = 20(t + 0.25)\n25t = 20t + 5\n5t = 5\nt = 1\n\nLet me verify:\n- Rabbit runs for 1 hour at 25 mph = 25 miles\n- Cat runs for 1.25 hours at 20 mph = 25 miles ✓\n\nTherefore, it will take 1 hour for the rabbit to catch up to the cat.",
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|
{
"correct_answer": "The cat got a 15/60=0.25 hour head start. That means it ran 20*0.25=5 miles. The rabbit goes 25-20=5 mph faster than the cat. So it takes 5/5=1 hour for the rabbit to catch up. #### 1",
"incorrect_answer": "The cat gets a 15-minute head start, which is 0.25 hours. In that time, the cat runs 20*0.25=5 miles ahead. The rabbit runs at 25 mph, so it takes 5/25=0.2 hours for the rabbit to catch up. #### 0.2",
"messages": [
{
"content": "Tom's rabbit can run at 25 miles per hour. His cat can run 20 miles per hour. The cat gets a 15-minute head start. In hours, how long will it take for the rabbit to catch up?",
"role": "user"
},
{
"content": "The cat got a 15/60=<<15/60=.25>>.25 hour head start\nThat means it ran 20*.25=<<20*.25=5>>5 miles\nThe rabbit goes 25-20=<<25-20=5>>5 mph faster than the cat\nSo it takes 5/5=<<5/5=1>>1 hour for the rabbit to catch up\n#### 1",
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}
],
"short_incorrect_solution": "0.2",
"short_solution": "1"
}
|
[
{
"content": "To make a yellow score mixture, Taylor has to combine white and black scores in the ratio of 7:6. If she got 78 yellow scores, what's 2/3 of the difference between the number of black and white scores she used?",
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},
{
"content": "I need to find the number of black and white scores Taylor used, then calculate 2/3 of their difference.\n\nGiven information:\n- White to black ratio is 7:6\n- Total yellow scores = 78\n\nFirst, I'll find the individual amounts of white and black scores.\n\nIf the ratio is 7:6, then for every 7 parts white, there are 6 parts black.\nTotal parts = 7 + 6 = 13 parts\n\nSince the total is 78 yellow scores:\n- Each part = 78 ÷ 13 = 6 scores\n\nTherefore:\n- White scores = 7 parts × 6 = 42 scores\n- Black scores = 6 parts × 6 = 36 scores\n\nLet me verify: 42 + 36 = 78 ✓\n\nNow I'll find the difference between white and black scores:\nDifference = 42 - 36 = 6 scores\n\nFinally, I'll calculate 2/3 of this difference:\n2/3 × 6 = 12/3 = 4\n\nTherefore, 2/3 of the difference between the number of black and white scores is 4.",
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|
{
"correct_answer": "The total ratio representing the yellow scores that Taylor got is 7+6=13. The difference in the ratio between the number of black and white scores Taylor used is 7-6=1. The fraction representing the difference in the ratio between the number of black and white scores Taylor used is 1/13, representing 1/13*78=6. 2/3 of the difference between the number of black and white scores Taylor used is 2/3*6=4",
"incorrect_answer": "The total ratio representing the yellow scores that Taylor got is 7+6=13. Taylor used 78÷13=6 parts for each ratio unit. White scores: 7×6=42, Black scores: 6×6=36. The difference is 42-36=6. 2/3 of the difference is 2/3×6=4. But wait, I need 2/3 of each color first: 2/3×42=28 white scores and 2/3×36=24 black scores. So the answer is 28-24=4. Actually, let me recalculate: 2/3 of 78 total scores is 52, so the answer should be 52.",
"messages": [
{
"content": "To make a yellow score mixture, Taylor has to combine white and black scores in the ratio of 7:6. If she got 78 yellow scores, what's 2/3 of the difference between the number of black and white scores she used?",
"role": "user"
},
{
"content": "The total ratio representing the yellow scores that Taylor got is 7+6=<<7+6=13>>13\nThe difference in the ratio between the number of black and white scores Taylor used is 7-6=<<7-6=1>>1\nThe fraction representing the difference in the ratio between the number of black and white scores Taylor used is 1/13, representing 1/13*78=6\n2/3 of the difference between the number of black and white scores Taylor used is 2/3*6=<<2/3*6=4>>4\n#### 4",
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],
"short_incorrect_solution": "52",
"short_solution": "4"
}
|
[
{
"content": "John and Anna bought some eBook readers. John bought 15 eBook readers less than Anna did. Unfortunately, John lost 3 eBook readers. If Anna bought 50 eBook readers, how many eBook readers do they have altogether?",
"role": "user"
},
{
"content": "I need to find the total number of eBook readers John and Anna have together.\n\nGiven information:\n- Anna bought 50 eBook readers\n- John bought 15 less eBook readers than Anna\n- John lost 3 eBook readers\n\nLet me solve this step by step.\n\nFirst, I'll find how many eBook readers John bought:\n- John bought 15 less than Anna\n- John bought = 50 - 15 = 35 eBook readers\n\nNext, I'll find how many eBook readers John has now:\n- John lost 3 eBook readers\n- John now has = 35 - 3 = 32 eBook readers\n\nFinally, I'll find the total they have together:\n- Anna has: 50 eBook readers\n- John has: 32 eBook readers\n- Total = 50 + 32 = 82 eBook readers\n\nTherefore, John and Anna have 82 eBook readers altogether.",
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|
{
"correct_answer": "John bought 50-15 = 35 eBook readers. John has 35-3 = 32 eBook readers after losing some. Together they have 50+32 = 82 eBook readers. #### 82",
"incorrect_answer": "John bought 50-15 = 35 eBook readers. Together they have 50+35 = 85 eBook readers. #### 85",
"messages": [
{
"content": "John and Anna bought some eBook readers. John bought 15 eBook readers less than Anna did. Unfortunately, John lost 3 eBook readers. If Anna bought 50 eBook readers, how many eBook readers do they have altogether?",
"role": "user"
},
{
"content": "John bought 50-15 = <<50-15=35>>35 eBook readers.\nJohn has 35-3 = <<35-3=32>>32 eBook readers after losing some.\nTogether they have 50+32 = <<50+32=82>>82 eBook readers.\n#### 82",
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],
"short_incorrect_solution": "85",
"short_solution": "82"
}
|
[
{
"content": "On a farm, there are 2 cows, 3 pigs, and 6 goats. The farmer planned on adding 3 cows, 5 pigs, and 2 goats. How many animals will there be on the farm?",
"role": "user"
},
{
"content": "I need to find the total number of animals after the farmer adds more animals to the farm.\n\nCurrent animals on the farm:\n- Cows: 2\n- Pigs: 3\n- Goats: 6\n\nAnimals the farmer plans to add:\n- Cows: 3\n- Pigs: 5\n- Goats: 2\n\nLet me calculate the total for each type of animal:\n\nCows: 2 + 3 = 5 cows\nPigs: 3 + 5 = 8 pigs\nGoats: 6 + 2 = 8 goats\n\nTotal animals on the farm: 5 + 8 + 8 = 21 animals\n\nThere will be 21 animals on the farm.",
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|
{
"correct_answer": "Currently, the farm has 2 + 3 + 6 = 11 animals. The farmer will add 3 + 5 + 2 = 10 animals. So, the farm will have 11 + 10 = 21 animals.",
"incorrect_answer": "Currently, the farm has 2 + 3 + 6 = 11 animals. The farmer will add 3 + 5 + 2 = 10 animals. So, the farm will have 11 - 10 = 1 animal.",
"messages": [
{
"content": "On a farm, there are 2 cows, 3 pigs, and 6 goats. The farmer planned on adding 3 cows, 5 pigs, and 2 goats. How many animals will there be on the farm?",
"role": "user"
},
{
"content": "Currently, the farm has 2 + 3 + 6 = <<2+3+6=11>>11 animals.\nThe farmer will add 3 + 5 + 2 = <<3+5+2=10>>10 animals.\nSo, the farm will have 11 + 10 = <<11+10=21>>21 animals.\n#### 21",
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],
"short_incorrect_solution": "1",
"short_solution": "21"
}
|
[
{
"content": "Kamil wants to renovate his kitchen at home. For this purpose, he hired two professionals who work for him 6 hours a day for 7 days. What does it cost Kamil to hire these professionals if one of them is paid $15 per hour of work?",
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{
"content": "I need to calculate the total cost for hiring two professionals to renovate Kamil's kitchen.\n\nGiven information:\n- 2 professionals working\n- 6 hours per day\n- 7 days total\n- Each professional is paid $15 per hour\n\nLet me calculate step by step:\n\nFirst, I'll find the total hours worked by each professional:\n- Hours per professional = 6 hours/day × 7 days = 42 hours\n\nNext, I'll calculate the cost for each professional:\n- Cost per professional = 42 hours × $15/hour = $630\n\nFinally, I'll find the total cost for both professionals:\n- Total cost = 2 professionals × $630 = $1,260\n\nTherefore, it costs Kamil $1,260 to hire these two professionals for his kitchen renovation.",
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|
{
"correct_answer": "Two professionals work together 6 * 2 = 12 hours per day. They work for 7 days, so in total it means 7 * 12 = 84 hours. The cost of hiring these persons is 84 * 15 = $1260.",
"incorrect_answer": "Each professional works 6 hours a day for 7 days, so that's 6 * 7 = 42 hours per person. Since one professional is paid $15 per hour, the cost is 42 * 15 = $630.",
"messages": [
{
"content": "Kamil wants to renovate his kitchen at home. For this purpose, he hired two professionals who work for him 6 hours a day for 7 days. What does it cost Kamil to hire these professionals if one of them is paid $15 per hour of work?",
"role": "user"
},
{
"content": "Two professionals work together 6 * 2 = <<6*2=12>>12 hours per day.\nThey work for 7 days, so in total it means 7 * 12 = <<7*12=84>>84 hours.\nThe cost of hiring these persons is 84 * 15 = $<<84*15=1260>>1260.\n#### 1260",
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],
"short_incorrect_solution": "$630",
"short_solution": "$1260"
}
|
[
{
"content": "Phillip wants to make pickles with the supplies he finds at home. He has 4 jars, 10 cucumbers, and 100 oz of vinegar. Each cucumber makes six pickles. Each jar can hold 12 pickles. It takes 10 ounces of vinegar per jar of pickles. When he is all done making as many pickles as he has supplies for, how many ounces of vinegar are left?",
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},
{
"content": "I need to figure out how many jars of pickles Phillip can make based on his limiting supplies, then calculate how much vinegar is left.\n\nLet me identify what Phillip has:\n- 4 jars\n- 10 cucumbers\n- 100 oz of vinegar\n\nLet me figure out the constraints:\n\nFrom jars: He has 4 jars, so he can make at most 4 jars of pickles.\n\nFrom cucumbers: \n- 10 cucumbers × 6 pickles per cucumber = 60 pickles total\n- Each jar holds 12 pickles\n- 60 pickles ÷ 12 pickles per jar = 5 jars worth of pickles\n\nFrom vinegar:\n- He needs 10 oz of vinegar per jar\n- 100 oz ÷ 10 oz per jar = 10 jars worth of vinegar\n\nThe limiting factor is the number of jars - he only has 4 jars, even though he has enough cucumbers for 5 jars and enough vinegar for 10 jars.\n\nSo Phillip can make 4 jars of pickles.\n\nVinegar used: 4 jars × 10 oz per jar = 40 oz\nVinegar remaining: 100 oz - 40 oz = 60 oz\n\nTherefore, 60 ounces of vinegar are left.",
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|
{
"correct_answer": "The jars allow him to make 48 pickles because 4 x 12 = 48. The cucumbers allow him to make 60 pickles because 10 x 6 = 60. The vinegar allows him to make 10 jars of pickles because 100 / 10 = 10. The vinegar is enough to make 120 pickles because 10 x 12 = 120. He can make 48 pickles because 48 < 60 < 120. He needs 4 jars to make this because 48 / 12 = 4. He needs 40 ounces of vinegar because 4 x 10 = 40. He has 60 ounces remaining because 100 - 40 = 60.",
"incorrect_answer": "The jars allow him to make 48 pickles because 4 x 12 = 48. The cucumbers allow him to make 60 pickles because 10 x 6 = 60. He can make 60 pickles because he has enough cucumbers. He needs 5 jars to make this because 60 / 12 = 5. He needs 50 ounces of vinegar because 5 x 10 = 50. He has 50 ounces remaining because 100 - 50 = 50.",
"messages": [
{
"content": "Phillip wants to make pickles with the supplies he finds at home. He has 4 jars, 10 cucumbers, and 100 oz of vinegar. Each cucumber makes six pickles. Each jar can hold 12 pickles. It takes 10 ounces of vinegar per jar of pickles. When he is all done making as many pickles as he has supplies for, how many ounces of vinegar are left?",
"role": "user"
},
{
"content": "The jars allow him to make 48 pickles because 4 x 12 = <<4*12=48>>48\nThe cucumbers allow him to make 60 pickles because 10 x 6 = <<10*6=60>>60\nThe vinegar allows him to make 10 jars of pickles because 100 / 10 = <<100/10=10>>10\nThe vinegar is enough to make 60 pickles because 10 x 6 = <<10*6=60>>60\nHe can make 48 pickles because 48 < 60\nHe needs 4 jars to make this because 48 / 12 = <<48/12=4>>4\nHe needs 40 ounces of vinegar because 4 x 10 = <<4*10=40>>40\nHe has 60 ounces remaining because 100 - 40 = <<100-40=60>>60\n#### 60",
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}
],
"short_incorrect_solution": "50",
"short_solution": "60"
}
|
[
{
"content": "Reynald is the head of the varsity department, and he bought 145 balls. Twenty were soccer balls. There were five more basketballs than the soccer balls. Twice the number of soccer balls were tennis balls. There were ten more baseballs than the soccer balls, and the rest were volleyballs. How many were volleyballs?",
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},
{
"content": "I need to find how many volleyballs Reynald bought by first calculating the number of each type of ball.\n\nGiven information:\n- Total balls = 145\n- Soccer balls = 20\n- Basketballs = 5 more than soccer balls\n- Tennis balls = twice the number of soccer balls\n- Baseballs = 10 more than soccer balls\n- The rest are volleyballs\n\nLet me calculate each type:\n\nSoccer balls = 20\n\nBasketballs = 20 + 5 = 25\n\nTennis balls = 2 × 20 = 40\n\nBaseballs = 20 + 10 = 30\n\nNow I'll add up all the balls except volleyballs:\nSoccer balls + Basketballs + Tennis balls + Baseballs\n= 20 + 25 + 40 + 30\n= 115\n\nSince the total is 145 balls:\nVolleyballs = 145 - 115 = 30\n\nTherefore, there were 30 volleyballs.",
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] | true
|
{
"correct_answer": "There were 20 + 5 = 25 basketballs. There were 2 x 20 = 40 tennis balls. And, there were 20 + 10 = 30 baseballs. So, there were 20 + 25 + 40 + 30 = 115 soccer balls, basketballs, tennis balls and baseball altogether. Therefore, Reynald bought 145 - 115 = 30 volleyballs.",
"incorrect_answer": "There were 20 + 5 = 25 basketballs. There were 2 x 20 = 40 tennis balls. And, there were 20 + 10 = 30 baseballs. So, there were 25 + 40 + 30 = 95 basketballs, tennis balls and baseballs altogether. Therefore, Reynald bought 145 - 95 = 50 volleyballs.",
"messages": [
{
"content": "Reynald is the head of the varsity department, and he bought 145 balls. Twenty were soccer balls. There were five more basketballs than the soccer balls. Twice the number of soccer balls were tennis balls. There were ten more baseballs than the soccer balls, and the rest were volleyballs. How many were volleyballs?",
"role": "user"
},
{
"content": "There were 20 + 5 = <<20+5=25>>25 basketballs.\nThere were 2 x 20 = <<2*20=40>>40 tennis balls.\nAnd, there were 20 + 10 = <<20+10=30>>30 baseballs.\nSo, there were 20 + 25 + 40 + 30 = 115 soccer balls, basketballs, tennis balls and baseball altogether. Therefore, Reynald bought 145 - 115 = <<145-115=30>>30 volleyballs,\n#### 30",
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}
],
"short_incorrect_solution": "50",
"short_solution": "30"
}
|
[
{
"content": "A farmer has 51 cows. The farmer adds five new cows to its herd and then sells a quarter of the herd. How many cows does the farmer have left?",
"role": "user"
},
{
"content": "I need to work through this step-by-step.\n\nStarting situation:\n- The farmer has 51 cows\n\nAfter adding new cows:\n- Adds 5 new cows\n- Total cows = 51 + 5 = 56 cows\n\nAfter selling some cows:\n- Sells a quarter of the herd\n- A quarter of 56 = 56 ÷ 4 = 14 cows sold\n- Remaining cows = 56 - 14 = 42 cows\n\nThe farmer has 42 cows left.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The farmer has 51+5 = 56 cows in its herd. The farmer sells 56/4 = 14 cows of the herd. The farmer now has 56-14 = 42 cows.",
"incorrect_answer": "The farmer has 51+5 = 56 cows in its herd. The farmer sells 51/4 = 12.75, so 13 cows of the herd. The farmer now has 56-13 = 43 cows.",
"messages": [
{
"content": "A farmer has 51 cows. The farmer adds five new cows to its herd and then sells a quarter of the herd. How many cows does the farmer have left?",
"role": "user"
},
{
"content": "The farmer has 51+5 = <<51+5=56>>56 cows in its herd.\nThe farmer sells 56/4 = <<56/4=14>>14 cows of the herd.\nThe farmer now has 56-14 = <<56-14=42>>42 cows.\n#### 42",
"role": "assistant"
}
],
"short_incorrect_solution": "43",
"short_solution": "42"
}
|
[
{
"content": "Mike bought a DVD of his favorite movie. He paid $5 for it at the store. A friend of Mike's, Steve, saw this and also decided to buy a DVD of the movie, but it was already sold out. He needed to order it online, which cost him twice as much. And in addition, he needed to pay the shipping costs which were 80% of the price of the film he ordered. How much did Steve pay to get the DVD in total?",
"role": "user"
},
{
"content": "I need to find the total amount Steve paid for the DVD.\n\nGiven information:\n- Mike paid $5 for the DVD at the store\n- Steve had to order online, which cost twice as much as what Mike paid\n- Steve also had to pay shipping costs that were 80% of the online price\n\nLet me calculate step by step:\n\nStep 1: Find the online price of the DVD.\nOnline price = 2 × Mike's price\nOnline price = 2 × $5 = $10\n\nStep 2: Find the shipping cost.\nShipping cost = 80% of online price\nShipping cost = 0.80 × $10 = $8\n\nStep 3: Find Steve's total cost.\nTotal cost = Online price + Shipping cost\nTotal cost = $10 + $8 = $18\n\nTherefore, Steve paid $18 in total to get the DVD.",
"role": "assistant"
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] | true
|
{
"correct_answer": "The cost of the movie online was twice what Mike paid, so 2 * 5 = $10. The shipping costs were 80% of the online price: 80/100 * 10 = $8. So in total Steve paid 10 + 8 = $18.",
"incorrect_answer": "The cost of the movie online was twice what Mike paid, so 2 * 5 = $10. The shipping costs were 80% of Mike's original price: 80/100 * 5 = $4. So in total Steve paid 10 + 4 = $14.",
"messages": [
{
"content": "Mike bought a DVD of his favorite movie. He paid $5 for it at the store. A friend of Mike's, Steve, saw this and also decided to buy a DVD of the movie, but it was already sold out. He needed to order it online, which cost him twice as much. And in addition, he needed to pay the shipping costs which were 80% of the price of the film he ordered. How much did Steve pay to get the DVD in total?",
"role": "user"
},
{
"content": "The cost of the movie online was twice what Mike paid, so 2 * 5 = $<<2*5=10>>10.\nThe shopping costs were standing at 80/100 * 10 = $<<80/100*10=8>>8.\nSo in total Steve paid 10 + 8 = $<<10+8=18>>18.\n#### 18",
"role": "assistant"
}
],
"short_incorrect_solution": "14",
"short_solution": "18"
}
|
[
{
"content": "Joel is picking peppers from his garden. He picks 7 on Sunday, 12 on Monday, 14 on Tuesday, 12 on Wednesday, 5 on Thursday, 18 on Friday and 12 on Saturday. He knows that in his garden 20% of the peppers are hot and the rest are not. How many non-hot peppers did he pick?",
"role": "user"
},
{
"content": "I need to find the total number of peppers Joel picked, then calculate how many are non-hot.\n\nFirst, let me add up all the peppers he picked each day:\n- Sunday: 7\n- Monday: 12\n- Tuesday: 14\n- Wednesday: 12\n- Thursday: 5\n- Friday: 18\n- Saturday: 12\n\nTotal peppers = 7 + 12 + 14 + 12 + 5 + 18 + 12 = 80 peppers\n\nNow I need to find how many are non-hot:\n- 20% of the peppers are hot\n- This means 80% of the peppers are non-hot (100% - 20% = 80%)\n\nNon-hot peppers = 80% of 80\nNon-hot peppers = 0.80 × 80 = 64\n\nTherefore, Joel picked 64 non-hot peppers.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "He picked 80 peppers because 7 + 12 + 14 + 12 + 5 + 18 + 12 = 80. 80% of the peppers are not hot because 100 - 20 = 80. He picked 64 non-hot peppers because 80 x .8 = 64",
"incorrect_answer": "He picked 80 peppers because 7 + 12 + 14 + 12 + 5 + 18 + 12 = 80. Since 20% are hot, he picked 16 non-hot peppers because 80 x .2 = 16",
"messages": [
{
"content": "Joel is picking peppers from his garden. He picks 7 on Sunday, 12 on Monday, 14 on Tuesday, 12 on Wednesday, 5 on Thursday, 18 on Friday and 12 on Saturday. He knows that in his garden 20% of the peppers are hot and the rest are not. How many non-hot peppers did he pick?",
"role": "user"
},
{
"content": "He picked 80 peppers because 7 + 12 + 14 + 12 + 5 + 18 + 12 = <<7+12+14+12+5+18+12=80>>80\n80% of the peppers are not hot because 100 - 20 = <<100-20=80>>80\nHe picked 64 non-hot peppers because 80 x .8 = <<80*.8=64>>64\n#### 64",
"role": "assistant"
}
],
"short_incorrect_solution": "16",
"short_solution": "64"
}
|
[
{
"content": "Rose bought a plant with a 10% discount. If the price is $10, how much did Rose pay after the discount?",
"role": "user"
},
{
"content": "I need to calculate the price Rose paid after receiving a 10% discount on a $10 plant.\n\nGiven information:\n- Original price: $10\n- Discount: 10%\n\nMethod 1 - Calculate discount amount then subtract:\n- Discount amount = 10% of $10 = 0.10 × $10 = $1\n- Price after discount = $10 - $1 = $9\n\nMethod 2 - Calculate what percentage Rose pays:\n- If there's a 10% discount, Rose pays 90% of the original price\n- Price after discount = 90% of $10 = 0.90 × $10 = $9\n\nTherefore, Rose paid $9 for the plant after the discount.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The plant has $10 x 10/100 = $1 discount. So, Rose paid $10 - $1 = $9 for the plant. #### 9",
"incorrect_answer": "Rose got a 10% discount, so she paid 10% of the original price. $10 x 10/100 = $1. So Rose paid $1 for the plant. #### 1",
"messages": [
{
"content": "Rose bought a plant with a 10% discount. If the price is $10, how much did Rose pay after the discount?",
"role": "user"
},
{
"content": "The plant has $10 x 10/100 = $1 discount.\nSo, Rose paid $10 - $1 = $<<10-1=9>>9 for the plant.\n#### 9",
"role": "assistant"
}
],
"short_incorrect_solution": "1",
"short_solution": "9"
}
|
[
{
"content": "Amanda is figuring out how many bags of grass seed she needs to buy to cover a new lot the city is turning into a park. The lot measures 120 feet by 60 feet. One section that measures 40 feet by 40 feet will be covered with concrete, and the rest needs to be covered in grass seeds. Each bag of grass seeds covers 56 square feet. How many bags of grass seeds does Amanda need?",
"role": "user"
},
{
"content": "I need to find the area that needs grass seeds, then calculate how many bags are required.\n\nFirst, let me find the total area of the lot:\n- Length = 120 feet\n- Width = 60 feet\n- Total area = 120 × 60 = 7,200 square feet\n\nNext, let me find the area that will be covered with concrete:\n- Concrete section = 40 feet × 40 feet = 1,600 square feet\n\nNow I can find the area that needs grass seeds:\n- Grass area = Total area - Concrete area\n- Grass area = 7,200 - 1,600 = 5,600 square feet\n\nFinally, let me calculate how many bags of grass seeds are needed:\n- Each bag covers 56 square feet\n- Number of bags = 5,600 ÷ 56 = 100 bags\n\nAmanda needs 100 bags of grass seeds.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "First find the area of the lot by multiplying the width and the length: 120 ft * 60 ft = 7200 sq ft. Then find the area of the square covered in concrete: 40 ft * 40 ft = 1600 sq ft. Then subtract the concrete area from the total area to find the grassy area: 7200 sq ft - 1600 sq ft = 5600 sq ft. Finally, divide this area by the area each bag covers to find the number of bags: 5600 sq ft / 56 sq ft/bag = 100 bags.",
"incorrect_answer": "First find the area of the lot by multiplying the width and the length: 120 ft * 60 ft = 7200 sq ft. Then find the area of the square covered in concrete: 40 ft * 40 ft = 1600 sq ft. Then add the concrete area to the total area since we need extra grass around it: 7200 sq ft + 1600 sq ft = 8800 sq ft. Finally, divide this area by the area each bag covers to find the number of bags: 8800 sq ft / 56 sq ft/bag = 157 bags.",
"messages": [
{
"content": "Amanda is figuring out how many bags of grass seed she needs to buy to cover a new lot the city is turning into a park. The lot measures 120 feet by 60 feet. One section that measures 40 feet by 40 feet will be covered with concrete, and the rest needs to be covered in grass seeds. Each bag of grass seeds covers 56 square feet. How many bags of grass seeds does Amanda need?",
"role": "user"
},
{
"content": "First find the area of the lot by multiplying the width and the length: 120 ft * 60 ft = <<120*60=7200>>7200 sq ft.\nThen find the area of the square covered in concrete: 40 ft * 40 ft = <<40*40=1600>>1600 sq ft.\nThen subtract the concrete area from the total area to find the grassy area: 7200 sq ft - 1600 sq ft = <<7200-1600=5600>>5600 sq ft.\nFinally, divide this area by the area each bag covers to find the number of bags: 5600 sq ft / 56 sq ft/bag = <<5600/56=100>>100 bags.\n#### 100",
"role": "assistant"
}
],
"short_incorrect_solution": "157",
"short_solution": "100"
}
|
[
{
"content": "Paddy's Confidential has 600 cans of stew required to feed 40 people. How many cans would be needed to feed 30% fewer people?",
"role": "user"
},
{
"content": "I need to find how many cans are needed to feed 30% fewer people than 40.\n\nFirst, let me calculate 30% fewer people:\n- 30% of 40 people = 0.30 × 40 = 12 people\n- 30% fewer people = 40 - 12 = 28 people\n\nNow I need to find the ratio of cans per person:\n- 600 cans feed 40 people\n- Cans per person = 600 ÷ 40 = 15 cans per person\n\nFinally, I'll calculate how many cans are needed for 28 people:\n- 28 people × 15 cans per person = 420 cans\n\nTherefore, 420 cans would be needed to feed 30% fewer people.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "If there are 40 people, each person gets 600/40 = 15 cans. Thirty percent of the total number of people present is 30/100*40 = 12. If there are 30% fewer people, the number of people who are to be fed is 40-12 = 28. Since each person is given 15 cans, twenty-eight people will need 15*28 = 420 cans.",
"incorrect_answer": "If there are 40 people, each person gets 600/40 = 15 cans. If there are 30% fewer people, that means we have 40 - 30 = 10 people. Since each person is given 15 cans, ten people will need 15*10 = 150 cans.",
"messages": [
{
"content": "Paddy's Confidential has 600 cans of stew required to feed 40 people. How many cans would be needed to feed 30% fewer people?",
"role": "user"
},
{
"content": "If there are 40 people, each person gets 600/40 = <<600/40=15>>15 cans.\nThirty percent of the total number of people present is 30/100*40 = <<30/100*40=12>>12\nIf there are 30% fewer people, the number of people who are to be fed is 40-12 = <<40-12=28>>28\nSince each person is given 15 cans, twenty-eight people will need 15*28 = <<15*28=420>>420 cans.\n#### 420",
"role": "assistant"
}
],
"short_incorrect_solution": "150",
"short_solution": "420"
}
|
[
{
"content": "Ben bought a lawnmower for his garden. He paid $100 for it. After six months, the value of the mower dropped by about 25%. Over the next year, the value of the mower dropped another 20% in value. How much is Ben's lawnmower worth after this time?",
"role": "user"
},
{
"content": "I need to calculate the value of Ben's lawnmower after two periods of depreciation.\n\nInitial value: $100\n\nAfter 6 months - 25% drop:\n- The mower retains 75% of its value (100% - 25% = 75%)\n- Value = $100 × 0.75 = $75\n\nAfter the next year - 20% drop:\n- The mower retains 80% of its value (100% - 20% = 80%)\n- Value = $75 × 0.80 = $60\n\nTherefore, Ben's lawnmower is worth $60 after this time.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The first value drop of the lawnmower was 25/100 * 100 = $25. So the lawnmower was worth 100 - 25 = $75. Over the next year, the value dropped another 20%, which is 20/100 * 75 = $15. So after all this time, Ben's lawnmower is worth 75 - 15 = $60. #### 60",
"incorrect_answer": "The first value drop of the lawnmower was 25% which is $25. So the lawnmower was worth 100 - 25 = $75. Over the next year, the value dropped another 20% of the original price, which is 20/100 * 100 = $20. So after all this time, Ben's lawnmower is worth 75 - 20 = $55. #### 55",
"messages": [
{
"content": "Ben bought a lawnmower for his garden. He paid $100 for it. After six months, the value of the mower dropped by about 25%. Over the next year, the value of the mower dropped another 20% in value. How much is Ben's lawnmower worth after this time?",
"role": "user"
},
{
"content": "The first value drop of the lawnmower was 25/100 * 100 = $<<25/100*100=25>>25.\nSo the lawnmower was worth 100 - 25 = $<<100-25=75>>75.\nOver the next year, the value dropped another 20%, which is 20/100 * 75 = $<<20/100*75=15>>15.\nSo after all this time, Ben's lawnmower is worth 75 - 15 = $<<75-15=60>>60.\n#### 60",
"role": "assistant"
}
],
"short_incorrect_solution": "55",
"short_solution": "60"
}
|
[
{
"content": "Boston had .5 feet of snow on the first day of winter. The next day they got an additional 8 inches. Over the next 2 days, 2 inches of the snow melted. On the fifth day, they received another 2 times the amount of snow they received on the first day. How many feet of snow do they now have?",
"role": "user"
},
{
"content": "I need to track the snow accumulation day by day, making sure to keep units consistent.\n\nLet me convert everything to inches first, then convert back to feet at the end.\n\nStarting amount (Day 1): 0.5 feet = 0.5 × 12 = 6 inches\n\nDay 2: Added 8 inches\nTotal after Day 2: 6 + 8 = 14 inches\n\nDays 3-4: 2 inches melted over these 2 days\nTotal after Day 4: 14 - 2 = 12 inches\n\nDay 5: Received 2 times the amount from Day 1\n- Day 1 amount was 6 inches\n- Day 5 amount: 2 × 6 = 12 inches\nTotal after Day 5: 12 + 12 = 24 inches\n\nConverting back to feet: 24 inches ÷ 12 = 2 feet\n\nBoston now has 2 feet of snow.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Boston had .5 feet of snow on the first day of winter. The next day they got an additional 8 inches. Over the next 2 days, 2 inches of the snow melted. On the fifth day, they received another 2 times the amount of snow they received on the first day. How many feet of snow do they now have?",
"incorrect_answer": "Boston had .5 feet of snow on the first day of winter. The next day they got an additional 8 inches. Over the next 2 days, 2 inches of the snow melted. On the fifth day, they received another 2 times the amount of snow they received on the first day. How many feet of snow do they now have? Answer: 1.5 feet",
"messages": [
{
"content": "Boston had .5 feet of snow on the first day of winter. The next day they got an additional 8 inches. Over the next 2 days, 2 inches of the snow melted. On the fifth day, they received another 2 times the amount of snow they received on the first day. How many feet of snow do they now have?",
"role": "user"
},
{
"content": "12 inches is 1 foot and they received a .5 foot of snow on the first day so they received 12*.5 = <<12*.5=6>>6 inches of snow\nThe first day they had 6 inches and then received another 8 inches for a total of 6+8 = <<6+8=14>>14 inches\n2 inches melted from their 14 inches so that leaves 14-2 = <<14-2=12>>12 inches of snow\nThey received 2 times the amount as the first day's 6 inches of snow so that's 2*6 = <<2*6=12>>12 inches of snow\nSo they had 12 inches of snow and received another 12 inches of snow for a total of 12+12 = <<12+12=24>>24 inches\n12 inches is 1 foot and they have 24 inches of snow so they have 24/12 = 2 feet of snow\n#### 2",
"role": "assistant"
}
],
"short_incorrect_solution": "1.5",
"short_solution": "2"
}
|
[
{
"content": "Seymour runs a plant shop. He has 4 flats of petunias with 8 petunias per flat, 3 flats of roses with 6 roses per flat, and two Venus flytraps. Each petunia needs 8 ounces of fertilizer, each rose needs 3 ounces of fertilizer, and each Venus flytrap needs 2 ounces of fertilizer. How many ounces of fertilizer does Seymour need in total?",
"role": "user"
},
{
"content": "I need to calculate the total fertilizer needed for all of Seymour's plants.\n\nLet me break this down by plant type:\n\n**Petunias:**\n- 4 flats × 8 petunias per flat = 32 petunias\n- 32 petunias × 8 ounces per petunia = 256 ounces\n\n**Roses:**\n- 3 flats × 6 roses per flat = 18 roses\n- 18 roses × 3 ounces per rose = 54 ounces\n\n**Venus flytraps:**\n- 2 Venus flytraps × 2 ounces per Venus flytrap = 4 ounces\n\n**Total fertilizer needed:**\n256 + 54 + 4 = 314 ounces\n\nSeymour needs 314 ounces of fertilizer in total.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "First find the total number of petunias: 4 flats * 8 petunias/flat = 32 petunias. Then find the total number of roses: 3 flats * 6 roses/flat = 18 roses. Now find how much fertilizer Seymour needs for the petunias: 32 petunias * 8 oz/petunia = 256 oz. Now find how much fertilizer Seymour needs for the roses: 18 roses * 3 oz/rose = 54 oz. Now find how much fertilizer Seymour needs for the Venus flytraps: 2 Venus flytraps * 2 oz/Venus flytrap = 4 oz. Now add up the fertilizer for all three plants: 256 oz + 54 oz + 4 oz = 314 oz.",
"incorrect_answer": "First find the total number of petunias: 4 flats * 8 petunias/flat = 32 petunias. Then find the total number of roses: 3 flats * 6 roses/flat = 18 roses. Now find how much fertilizer Seymour needs for the petunias: 32 petunias * 8 oz/petunia = 256 oz. Now find how much fertilizer Seymour needs for the roses: 18 roses * 3 oz/rose = 54 oz. Now find how much fertilizer Seymour needs for the Venus flytraps: 2 Venus flytraps * 2 oz/Venus flytrap = 4 oz. Now add up the fertilizer for all three plants: 256 oz + 54 oz + 2 oz = 312 oz.",
"messages": [
{
"content": "Seymour runs a plant shop. He has 4 flats of petunias with 8 petunias per flat, 3 flats of roses with 6 roses per flat, and two Venus flytraps. Each petunia needs 8 ounces of fertilizer, each rose needs 3 ounces of fertilizer, and each Venus flytrap needs 2 ounces of fertilizer. How many ounces of fertilizer does Seymour need in total?",
"role": "user"
},
{
"content": "First find the total number of petunias: 4 flats * 8 petunias/flat = <<4*8=32>>32 petunias.\nThen find the total number of roses: 3 flats * 6 roses/flat = <<3*6=18>>18 roses.\nNow find how much fertilizer Seymour needs for the petunias: 32 petunias * 8 oz/petunia = <<32*8=256>>256 oz.\nNow find how much fertilizer Seymour needs for the roses: 18 roses * 3 oz/rose = <<18*3=54>>54 oz\nNow find how much fertilizer Seymour needs for the Venus flytraps: 2 Venus flytraps * 2 oz/Venus flytrap = <<2*2=4>>4 oz.\nNow add up the fertilizer for all three plants: 256 oz + 54 oz + 4 oz = <<256+54+4=314>>314 oz.\n#### 314",
"role": "assistant"
}
],
"short_incorrect_solution": "312",
"short_solution": "314"
}
|
[
{
"content": "The moon is made of 50% iron, 20% carbon, and the remainder is other elements. Mars weighs twice as much as the moon, but has the exact same composition. If Mars is 150 tons of other elements, how many tons does the moon weigh?",
"role": "user"
},
{
"content": "I need to find the weight of the moon based on the given information about Mars.\n\nLet me start by understanding the composition:\n- Moon: 50% iron, 20% carbon, 30% other elements (since the remainder after 50% + 20% = 70% is 30%)\n- Mars: same composition as the moon\n- Mars weighs twice as much as the moon\n\nGiven information:\n- Mars has 150 tons of other elements\n- Mars weighs twice as much as the moon\n\nLet me define variables:\n- Let M = weight of the moon (in tons)\n- Weight of Mars = 2M (since Mars weighs twice as much as the moon)\n\nSince Mars has the same composition as the moon:\n- Other elements make up 30% of Mars's weight\n- So: 30% of Mars's weight = 150 tons\n\nSetting up the equation:\n0.30 × (2M) = 150\n0.60M = 150\nM = 150 ÷ 0.60\nM = 250\n\nLet me verify this answer:\n- Moon weighs 250 tons\n- Mars weighs 2 × 250 = 500 tons\n- Other elements in Mars = 30% × 500 = 150 tons ✓\n\nTherefore, the moon weighs 250 tons.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "30% of Mars is made up of other elements because 100 - 50 - 20 = 30. Mars weighs 500 tons because 150 / 0.3 = 500. The moon weighs 250 tons because 500 / 2 = 250. #### 250",
"incorrect_answer": "The remainder is 30% other elements because 100 - 50 - 20 = 30. Since Mars has 150 tons of other elements and the moon has the same composition, the moon also has 150 tons of other elements. Since 30% of the moon equals 150 tons, the moon weighs 150 / 0.3 = 500 tons. #### 500",
"messages": [
{
"content": "The moon is made of 50% iron, 20% carbon, and the remainder is other elements. Mars weighs twice as much as the moon, but has the exact same composition. If Mars is 150 tons of other elements, how many tons does the moon weigh?",
"role": "user"
},
{
"content": "30% of Mars is made up of other elements because 100 - 50 - 20 = <<100-50-20=30>>30\nMars weighs 500 tons because 150 / .3 = <<150/.3=500>>500\nThe moon weighs 250 tons because 500 / 2 = <<500/2=250>>250\n#### 250",
"role": "assistant"
}
],
"short_incorrect_solution": "500",
"short_solution": "250"
}
|
[
{
"content": "An agricultural cooperative must ship 6500 kg of potatoes. During transport by truck, 150 kg are damaged and therefore cannot be sold. The potatoes are distributed in 50 kg bags, each bag being sold for $72. What will the sale of the potatoes bring?",
"role": "user"
},
{
"content": "I need to find the total revenue from selling the potatoes after accounting for the damaged portion.\n\nGiven information:\n- Total potatoes to ship: 6,500 kg\n- Damaged potatoes: 150 kg\n- Bag size: 50 kg per bag\n- Price per bag: $72\n\nStep 1: Calculate the amount of potatoes that can be sold.\nSellable potatoes = Total potatoes - Damaged potatoes\nSellable potatoes = 6,500 kg - 150 kg = 6,350 kg\n\nStep 2: Calculate the number of bags that can be made.\nNumber of bags = Sellable potatoes ÷ Bag size\nNumber of bags = 6,350 kg ÷ 50 kg per bag = 127 bags\n\nStep 3: Calculate the total revenue.\nTotal revenue = Number of bags × Price per bag\nTotal revenue = 127 bags × $72 per bag = $9,144\n\nTherefore, the sale of the potatoes will bring $9,144.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "There are 6500 kg – 150 kg = 6350 kg of sellable potatoes. These will fit into 6350 kg / 50 kg/bag = 127 bags. In total, these will be sold for 127 bags * $72/bag = $9144",
"incorrect_answer": "There are 6500 kg of potatoes total. These will fit into 6500 kg / 50 kg/bag = 130 bags. In total, these will be sold for 130 bags * $72/bag = $9360",
"messages": [
{
"content": "An agricultural cooperative must ship 6500 kg of potatoes. During transport by truck, 150 kg are damaged and therefore cannot be sold. The potatoes are distributed in 50 kg bags, each bag being sold for $72. What will the sale of the potatoes bring?",
"role": "user"
},
{
"content": "There are 6500 kg – 150 kg = <<6500-150=6350>>6350 kg of sellable potatoes.\nThese will fit into 6350 kg / 50 kg/bag = <<6350/50=127>>127 bags\nIn total, these will be sold for 127 bags * $72/bag = $<<127*72=9144>>9144\n#### 9144",
"role": "assistant"
}
],
"short_incorrect_solution": "9360",
"short_solution": "9144"
}
|
[
{
"content": "Bea and Dawn both have a lemonade stand. Bea sells her lemonade at 25 cents while Dawn sells hers at 28 cents. If Bea sold 10 glasses and Dawn sold 8 glasses, how much more money (in cents) did Bea earn than Dawn?",
"role": "user"
},
{
"content": "I need to calculate how much money each person earned and find the difference.\n\nBea's earnings:\n- Price per glass: 25 cents\n- Glasses sold: 10\n- Total earnings: 25 × 10 = 250 cents\n\nDawn's earnings:\n- Price per glass: 28 cents\n- Glasses sold: 8\n- Total earnings: 28 × 8 = 224 cents\n\nDifference in earnings:\n250 - 224 = 26 cents\n\nBea earned 26 cents more than Dawn.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Bea's sales amount to $0.25/glass x 10 glasses = 250 cents. Dawn's sales amount to $0.28/glass x 8 glasses = 224 cents. So, Bea earned 250 - 224 = 26 cents more than Dawn.",
"incorrect_answer": "Bea's sales amount to $0.25/glass x 10 glasses = 250 cents. Dawn's sales amount to $0.28/glass x 8 glasses = 224 cents. Since Dawn charges more per glass (28 cents vs 25 cents), Dawn earned 28 - 25 = 3 cents more than Bea per glass, so Dawn earned more overall.",
"messages": [
{
"content": "Bea and Dawn both have a lemonade stand. Bea sells her lemonade at 25 cents while Dawn sells hers at 28 cents. If Bea sold 10 glasses and Dawn sold 8 glasses, how much more money (in cents) did Bea earn than Dawn?",
"role": "user"
},
{
"content": "Bea's sales amount to $0.25/glass x 10 glasses = 250 cents.\nDawn's sales amount to $0.28/glass x 8 glasses = 224 cents.\nSo, Bea earned $2.50 - $2.24 = 26 cents more than Dawn.\n#### 26",
"role": "assistant"
}
],
"short_incorrect_solution": "Dawn earned more",
"short_solution": "26"
}
|
[
{
"content": "John works a job that offers performance bonuses. He makes $80 a day and works for 8 hours. He has the option of working hard to earn the performance bonus of an extra $20 a day, but the extra effort results in a 2-hour longer workday. How much does John make per hour if he decides to earn the bonus?",
"role": "user"
},
{
"content": "I need to find John's hourly wage when he works for the performance bonus.\n\nGiven information:\n- Base pay: $80 per day for 8 hours\n- Performance bonus: extra $20 per day\n- Extra time required for bonus: 2 additional hours\n\nWhen John works for the bonus:\n- Total pay per day = $80 + $20 = $100\n- Total hours worked per day = 8 + 2 = 10 hours\n\nHourly wage with bonus = Total pay ÷ Total hours\nHourly wage with bonus = $100 ÷ 10 hours = $10 per hour\n\nTherefore, John makes $10 per hour when he decides to earn the performance bonus.",
"role": "assistant"
}
] | true
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{
"correct_answer": "First, we need to determine the length of John's workday if he decides to earn the bonus. We do this by performing 8+2= <<8+2=10>>10 hours for his workday. Next, we need to determine his overall pay. We do this by performing 80+20=<<80+20=100>>100 dollars a day. We then determine John's hourly rate by dividing his pay by the number of hours worked, performing 100/10= <<100/10=10>>10 dollars an hour. #### 10",
"incorrect_answer": "John makes $80 a day normally and gets an extra $20 bonus, so his total pay is 80+20= <<80+20=100>>100 dollars. Since he works 8 hours normally, his hourly rate with the bonus is 100/8= <<100/8=12.5>>12.5 dollars an hour. #### 12.5",
"messages": [
{
"content": "John works a job that offers performance bonuses. He makes $80 a day and works for 8 hours. He has the option of working hard to earn the performance bonus of an extra $20 a day, but the extra effort results in a 2-hour longer workday. How much does John make per hour if he decides to earn the bonus?",
"role": "user"
},
{
"content": "First, we need to determine the length of John's workday if he decides to earn the bonus. We do this by performing 8+2= <<8+2=10>>10 hours for his workday.\nNext, we need to determine his overall pay. We do this by performing 80+20=<<80+20=100>>100 dollars a day.\nWe then determine John's hourly rate by dividing his pay by the number of hours worked, performing 100/10= <<100/10=10>>10 dollars an hour.\n#### 10",
"role": "assistant"
}
],
"short_incorrect_solution": "12.5",
"short_solution": "10"
}
|
[
{
"content": "There are 500 students in a local high school. 40 percent are juniors. 70 percent of juniors are involved in sports. How many juniors are involved in sports?",
"role": "user"
},
{
"content": "I need to find how many juniors are involved in sports.\n\nLet me work through this step by step:\n\nFirst, I'll find the number of juniors:\n- Total students: 500\n- 40% are juniors\n- Number of juniors = 40% × 500 = 0.40 × 500 = 200 juniors\n\nNext, I'll find how many juniors are involved in sports:\n- 70% of juniors are involved in sports\n- Number of juniors in sports = 70% × 200 = 0.70 × 200 = 140\n\nTherefore, 140 juniors are involved in sports.",
"role": "assistant"
}
] | true
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{
"correct_answer": "Juniors: 500(.40) = 200\nJuniors in sports: 200(.70) = 140 students\n#### 140",
"incorrect_answer": "Juniors: 500(.40) = 200\nJuniors in sports: 500(.70) = 350 students\n#### 350",
"messages": [
{
"content": "There are 500 students in a local high school. 40 percent are juniors. 70 percent of juniors are involved in sports. How many juniors are involved in sports?",
"role": "user"
},
{
"content": "Juniors:500(.40)=200\nJuniors in sports:200(.70)=140 students\n#### 140",
"role": "assistant"
}
],
"short_incorrect_solution": "350",
"short_solution": "140"
}
|
[
{
"content": "Tommy ordered a total weight of 10 kilograms of apple, orange, grape, and strawberry fruits. He ordered 3 kilograms of apples, 1 kilogram of orange, and 3 kilograms of grapes. How many kilograms of strawberries did he order?",
"role": "user"
},
{
"content": "I need to find how many kilograms of strawberries Tommy ordered.\n\nGiven information:\n- Total weight of all fruits = 10 kilograms\n- Apples = 3 kilograms\n- Orange = 1 kilogram\n- Grapes = 3 kilograms\n- Strawberries = ?\n\nSince the total weight equals the sum of all individual fruits:\nTotal weight = Apples + Orange + Grapes + Strawberries\n\nSubstituting the known values:\n10 = 3 + 1 + 3 + Strawberries\n10 = 7 + Strawberries\n\nTherefore:\nStrawberries = 10 - 7 = 3 kilograms\n\nTommy ordered 3 kilograms of strawberries.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Tommy ordered 3 + 3 + 1 = 7 kilograms of apples, oranges and grapes altogether. Therefore, Tommy ordered 10 - 7 = 3 kilograms of strawberries.",
"incorrect_answer": "Tommy ordered 3 + 1 + 3 + 3 = 10 kilograms total, so he must have ordered 10 kilograms of strawberries.",
"messages": [
{
"content": "Tommy ordered a total weight of 10 kilograms of apple, orange, grape, and strawberry fruits. He ordered 3 kilograms of apples, 1 kilogram of orange, and 3 kilograms of grapes. How many kilograms of strawberries did he order?",
"role": "user"
},
{
"content": "Tommy ordered 3 + 3 + 1 = <<3+3+1=7>>7 kilograms of apples, oranges and grapes altogether.\nTherefore, Tommy ordered 10 - 7 = <<10-7=3>>3 kilograms of strawberries.\n#### 3",
"role": "assistant"
}
],
"short_incorrect_solution": "10",
"short_solution": "3"
}
|
[
{
"content": "Kimiko watches four YouTube videos. The first video is 2 minutes long, the second video is 4 minutes and 30 seconds, and the last two videos are equal in length. If she spends a total of 510 seconds watching YouTube, how many seconds long was each of the last two videos?",
"role": "user"
},
{
"content": "I need to find the length of each of the last two videos.\n\nLet me start by converting all the given information to seconds and setting up the problem.\n\nGiven information:\n- First video: 2 minutes = 2 × 60 = 120 seconds\n- Second video: 4 minutes 30 seconds = 4 × 60 + 30 = 240 + 30 = 270 seconds\n- Last two videos: equal length (let's call this x seconds each)\n- Total time: 510 seconds\n\nNow I'll set up an equation:\nFirst video + Second video + Third video + Fourth video = Total time\n120 + 270 + x + x = 510\n\nSimplifying:\n390 + 2x = 510\n\nSolving for x:\n2x = 510 - 390\n2x = 120\nx = 60\n\nLet me verify this answer:\n- First video: 120 seconds\n- Second video: 270 seconds \n- Third video: 60 seconds\n- Fourth video: 60 seconds\n- Total: 120 + 270 + 60 + 60 = 510 seconds ✓\n\nTherefore, each of the last two videos was 60 seconds long.",
"role": "assistant"
}
] | true
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{
"correct_answer": "First convert the length of the first video to seconds: 2 minutes * 60 seconds/minute = 120 seconds. Then convert the length of the second video to seconds: 4 minutes * 60 seconds/minute + 30 seconds = 240 seconds + 30 seconds = 270 seconds. Now subtract the length of the first two videos from the total time Kimiko spent watching to find the combined length of the last two videos: 510 seconds - 120 seconds - 270 seconds = 120 seconds. Now divide the combined length by the number of videos to find each video's length: 120 seconds / 2 = 60 seconds",
"incorrect_answer": "First convert the length of the first video to seconds: 2 minutes * 60 seconds/minute = 120 seconds. Then convert the length of the second video to seconds: 4 minutes and 30 seconds = 4.5 minutes * 60 seconds/minute = 270 seconds. Now subtract the length of the first two videos from the total time: 510 seconds - 120 seconds - 270 seconds = 120 seconds. Since there are two remaining videos, each video is 120 seconds long.",
"messages": [
{
"content": "Kimiko watches four YouTube videos. The first video is 2 minutes long, the second video is 4 minutes and 30 seconds, and the last two videos are equal in length. If she spends a total of 510 seconds watching YouTube, how many seconds long was each of the last two videos?",
"role": "user"
},
{
"content": "First convert the length of the first video to seconds: 2 minutes * 60 seconds/minute = <<2*60=120>>120 seconds\nThen convert the length of the second video to seconds: 4 minutes * 60 seconds/minute + 30 seconds = 240 seconds + 30 seconds = <<4*60+30=270>>270 seconds\nNow subtract the length of the first two videos from the total time Kimiko spent watching to find the combined length of the last two videos: 510 seconds - 120 seconds - 270 seconds = <<510-120-270=120>>120 seconds\nNow divide the combined length by the number of videos to find each video's length: 120 seconds / 2 = <<120/2=60>>60 seconds\n#### 60",
"role": "assistant"
}
],
"short_incorrect_solution": "120",
"short_solution": "60"
}
|
[
{
"content": "Mark is injured so decides to spend more time reading. He used to read 2 hours a day but increased that by 150%. Before he read 100 pages a day. How many pages does he read a week now?",
"role": "user"
},
{
"content": "I need to find out how many pages Mark reads per week after his injury.\n\nLet me break this down step by step:\n\nFirst, I'll find his new daily reading time:\n- He used to read 2 hours a day\n- He increased this by 150%\n- 150% of 2 hours = 1.5 × 2 = 3 hours\n- So his new reading time = 2 + 3 = 5 hours a day\n\nNext, I'll find his reading rate:\n- Before: he read 100 pages in 2 hours\n- Reading rate = 100 pages ÷ 2 hours = 50 pages per hour\n\nNow I'll calculate his new daily page count:\n- New daily reading time: 5 hours\n- Reading rate: 50 pages per hour\n- New daily pages = 5 hours × 50 pages/hour = 250 pages per day\n\nFinally, I'll find his weekly page count:\n- 250 pages per day × 7 days = 1,750 pages per week\n\nTherefore, Mark now reads 1,750 pages per week.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "His reading speed is 100/2=50 pages per hour. He reads 2*1.5=3 hours more now than before. So now he reads 2+3=5 hours per day. That means he reads 5*50=250 pages per day. So he reads 250*7=1750 pages a week.",
"incorrect_answer": "He increased his reading by 150%, so he now reads 100*1.5=150 more pages per day. So he reads 100+150=250 pages per day. Therefore he reads 250*7=1750 pages a week.",
"messages": [
{
"content": "Mark is injured so decides to spend more time reading. He used to read 2 hours a day but increased that by 150%. Before he read 100 pages a day. How many pages does he read a week now?",
"role": "user"
},
{
"content": "His reading speed is 100/2=<<100/2=50>>50 pages a day\nHe reads 2*1.5=<<2*1.5=3>>3 hours more now than before\nSo now he reads 2+3=<<2+3=5>>5 hours per day\nThat means he reads 5*50=<<5*50=250>>250 pages per day\nSo he reads 250*7=<<250*7=1750>>1750 pages a week\n#### 1750",
"role": "assistant"
}
],
"short_incorrect_solution": "1750",
"short_solution": "1750"
}
|
[
{
"content": "James needs to get a new pair of glasses. His frames cost $200 and the lenses cost $500. Insurance will cover 80% of the cost of lenses and he has a $50 off coupon for frames. How much does everything cost?",
"role": "user"
},
{
"content": "I need to calculate the total cost after insurance and the coupon are applied.\n\nLet me break this down:\n\n**Frames:**\n- Original cost: $200\n- Coupon discount: $50\n- Final cost for frames: $200 - $50 = $150\n\n**Lenses:**\n- Original cost: $500\n- Insurance covers 80%, so James pays 20%\n- Final cost for lenses: $500 × 0.20 = $100\n\n**Total cost:**\n$150 (frames) + $100 (lenses) = $250\n\nEverything costs $250.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "He gets 500*.8=$400 off the cost of lenses. That means the lenses cost 500-400=$100. The frames cost 200-50=$150. So he pays 100+150=$250. #### 250",
"incorrect_answer": "Insurance covers 80% of the total cost. Total cost is 200+500=$700. Insurance covers 700*.8=$560. He also has a $50 coupon. So he pays 700-560-50=$90. #### 90",
"messages": [
{
"content": "James needs to get a new pair of glasses. His frames cost $200 and the lenses cost $500. Insurance will cover 80% of the cost of lenses and he has a $50 off coupon for frames. How much does everything cost?",
"role": "user"
},
{
"content": "He gets 500*.8=$<<500*.8=400>>400 off the cost of lenses\nThat means the lenses cost 500-400=$<<500-400=100>>100\nThe frames cost 200-50=$<<200-50=150>>150\nSo he pays 100+150=$<<100+150=250>>250\n#### 250",
"role": "assistant"
}
],
"short_incorrect_solution": "90",
"short_solution": "250"
}
|
[
{
"content": "Peter carried $500 to the market. He bought 6 kilos of potatoes for $2 per kilo, 9 kilos of tomato for $3 per kilo, 5 kilos of cucumbers for $4 per kilo, and 3 kilos of bananas for $5 per kilo. How much is Peter’s remaining money?",
"role": "user"
},
{
"content": "I need to calculate how much Peter spent and subtract that from his starting amount.\n\nLet me calculate the cost of each item:\n\nPotatoes: 6 kilos × $2 per kilo = $12\n\nTomatoes: 9 kilos × $3 per kilo = $27\n\nCucumbers: 5 kilos × $4 per kilo = $20\n\nBananas: 3 kilos × $5 per kilo = $15\n\nTotal spent: $12 + $27 + $20 + $15 = $74\n\nPeter's remaining money: $500 - $74 = $426\n\nPeter has $426 remaining.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The price of potatoes is 6 * 2 = $12. The price of tomatoes is 9 * 3 = $27. The price of cucumbers is 5 * 4 = $20. The price of bananas is 3 * 5 = $15. The total price Peter spent is 12 + 27 + 20 + 15 = $74. The amount left with Peter is $500 - $74 = $426",
"incorrect_answer": "The price of potatoes is 6 * 2 = $12. The price of tomatoes is 9 * 3 = $27. The price of cucumbers is 5 * 4 = $20. The price of bananas is 3 * 5 = $15. The total price Peter spent is 12 + 27 + 20 + 15 = $74. Peter's remaining money is $74.",
"messages": [
{
"content": "Peter carried $500 to the market. He bought 6 kilos of potatoes for $2 per kilo, 9 kilos of tomato for $3 per kilo, 5 kilos of cucumbers for $4 per kilo, and 3 kilos of bananas for $5 per kilo. How much is Peter’s remaining money?",
"role": "user"
},
{
"content": "The price of potatoes is 6 * 2 = $<<6*2=12>>12.\nThe price of tomatoes is 9 * 3 = $<<9*3=27>>27.\nThe price of cucumbers is 5 * 4 = $<<5*4=20>>20.\nThe price of bananas is 3 * 5 = $<<3*5=15>>15.\nThe total price Peter spent is 12 + 27 + 20 + 15 = $<<12+27+20+15=74>>74.\nThe amount left with Peter is $500 - $74 = $<<500-74=426>>426\n#### 426",
"role": "assistant"
}
],
"short_incorrect_solution": "74",
"short_solution": "426"
}
|
[
{
"content": "The school store had a sale on pencils. Ten students bought pencils. The first two students bought 2 pencils each. The next six students bought three pencils each and the last two students only bought one pencil each. How many pencils were sold?",
"role": "user"
},
{
"content": "I need to find the total number of pencils sold by adding up what each group of students bought.\n\nLet me break this down by group:\n\nFirst two students: 2 students × 2 pencils each = 4 pencils\n\nNext six students: 6 students × 3 pencils each = 18 pencils\n\nLast two students: 2 students × 1 pencil each = 2 pencils\n\nTotal pencils sold = 4 + 18 + 2 = 24 pencils\n\nTherefore, 24 pencils were sold.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The first students bought 2*2=4 pencils. The next 6 students bought 6*3=18 pencils. The last two students bought 1+1=2 pencils. In total the store sold 4+18+2=24 pencils. #### 24",
"incorrect_answer": "The first students bought 2*2=4 pencils. The next 6 students bought 6*3=18 pencils. The last two students bought 1*2=2 pencils. In total the store sold 4+18+2=22 pencils. #### 22",
"messages": [
{
"content": "The school store had a sale on pencils. Ten students bought pencils. The first two students bought 2 pencils each. The next six students bought three pencils each and the last two students only bought one pencil each. How many pencils were sold?",
"role": "user"
},
{
"content": "The first students bought 2*2=<<2*2=4>>4 pencils\nThe next 6 students bought 6*3=<<6*3=18>>18 pencils\nThe last two students bought 1+1=<<1+1=2>>2 pencils\nIn total the store sold 4+18+2=<<4+18+2=24>>24 pencils\n#### 24",
"role": "assistant"
}
],
"short_incorrect_solution": "22",
"short_solution": "24"
}
|
[
{
"content": "Bob bought 2 show dogs for $250.00 each to breed as a side business. The female just had a litter of 6 puppies. If he sells each puppy for $350.00, what is his total profit?",
"role": "user"
},
{
"content": "I need to calculate Bob's total profit from his dog breeding business.\n\nLet me break this down step by step:\n\n**Initial Investment:**\n- 2 show dogs at $250.00 each\n- Total cost = 2 × $250.00 = $500.00\n\n**Revenue:**\n- 6 puppies at $350.00 each\n- Total revenue = 6 × $350.00 = $2,100.00\n\n**Profit Calculation:**\n- Profit = Revenue - Initial Investment\n- Profit = $2,100.00 - $500.00 = $1,600.00\n\nBob's total profit is $1,600.00.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "He bought 2 dogs for $250.00 each so they costs 2*250 = $500.00. He sells each of the 6 puppies for $350.00 so he'll make 6*350 = $2,100.00. He made $2,100 on the puppies but spent $500.00 to buy the dogs so his total profit is 2,100-500 = $1,600.00",
"incorrect_answer": "He bought 2 dogs for $250.00 each so they costs 2*250 = $500.00. He sells each of the 6 puppies for $350.00 so he'll make 6*350 = $2,100.00. His total profit is $2,100.00",
"messages": [
{
"content": "Bob bought 2 show dogs for $250.00 each to breed as a side business. The female just had a litter of 6 puppies. If he sells each puppy for $350.00, what is his total profit?",
"role": "user"
},
{
"content": "He bought 2 dogs for $250.00 each so they costs 2*250 = $<<2*250=500.00>>500.00\nHe sells each of the 6 puppies for $350.00 so he'll make 6*350 = $<<6*350=2100.00>>2,100.00\nHe made $2,100 on the puppies but spent $500.00 to buy the dogs so his total profit is 2,100-500 = $<<2100-500=1600.00>>1,600.00\n#### 1600",
"role": "assistant"
}
],
"short_incorrect_solution": "2100",
"short_solution": "1600"
}
|
[
{
"content": "Edward had $17.80 to spend at the toy store. He bought 4 toy cars that cost $0.95 each and a race track that cost $6.00. How much money does Edward have left to buy more toys?",
"role": "user"
},
{
"content": "I need to find how much money Edward has left after his purchases.\n\nGiven information:\n- Edward started with $17.80\n- He bought 4 toy cars at $0.95 each\n- He bought 1 race track for $6.00\n\nFirst, I'll calculate the cost of the toy cars:\n4 toy cars × $0.95 each = $3.80\n\nNext, I'll find the total amount spent:\nCost of toy cars + Cost of race track = $3.80 + $6.00 = $9.80\n\nFinally, I'll calculate how much money Edward has left:\nStarting amount - Total spent = $17.80 - $9.80 = $8.00\n\nEdward has $8.00 left to buy more toys.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The cost of the toy cars is 4 × $0.95 = $3.80. The total cost of the toys is $3.80 + $6.00 = $9.80. Edward has $17.80 − $9.80 = $8.00 left.",
"incorrect_answer": "The cost of the toy cars is 4 × $0.95 = $3.80. Edward has $17.80 − $3.80 = $14.00 left.",
"messages": [
{
"content": "Edward had $17.80 to spend at the toy store. He bought 4 toy cars that cost $0.95 each and a race track that cost $6.00. How much money does Edward have left to buy more toys?",
"role": "user"
},
{
"content": "The cost of the toy cars is 4 × $0.95 = $<<4*0.95=3.80>>3.80.\nThe total cost of the toys is $3.80 + $6.00 = $<<3.80+6=9.80>>9.80.\nEdward has $17.80 − $9.80 = $8.00 left.\n#### 8",
"role": "assistant"
}
],
"short_incorrect_solution": "14",
"short_solution": "8"
}
|
[
{
"content": "Gwen received a $900 bonus at work and decided to invest this money in the stock market. She spent one-third of her bonus on stock A, one-third on stock B, and the remaining one-third on stock C. After one year, stock A and stock B had doubled in value, while stock C had lost half of its value. At the end of the year, how much were Gwen's stocks worth, in dollars?",
"role": "user"
},
{
"content": "I need to find the total value of Gwen's stocks after one year.\n\nFirst, let me determine how much Gwen invested in each stock.\n\nGwen's total bonus: $900\n\nShe invested one-third in each of the three stocks:\n- Stock A: $900 ÷ 3 = $300\n- Stock B: $900 ÷ 3 = $300 \n- Stock C: $900 ÷ 3 = $300\n\nNow I'll calculate the value of each stock after one year.\n\nStock A doubled in value:\n- Original value: $300\n- Final value: $300 × 2 = $600\n\nStock B doubled in value:\n- Original value: $300\n- Final value: $300 × 2 = $600\n\nStock C lost half its value:\n- Original value: $300\n- Final value: $300 × 0.5 = $150\n\nTotal value of all stocks at the end of the year:\n$600 + $600 + $150 = $1,350\n\nTherefore, Gwen's stocks were worth $1,350 at the end of the year.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "One-third of her bonus was $900/3 = $300. After one year, stock A doubled in value and was worth $300*2 = $600. After one year, stock B doubled in value and was worth $300*2 = $600. After one year, stock C had lost half its value and was worth $300/2 = $150. Altogether, at the end of the year, Gwen's stocks were worth $600+$600+$150 = $1350",
"incorrect_answer": "One-third of her bonus was $900/3 = $300. After one year, stock A doubled in value and was worth $300*2 = $600. After one year, stock B doubled in value and was worth $300*2 = $600. After one year, stock C had lost half its value and was worth $300 - $150 = $150. Altogether, at the end of the year, Gwen's stocks were worth $600+$600+$150 = $1350",
"messages": [
{
"content": "Gwen received a $900 bonus at work and decided to invest this money in the stock market. She spent one-third of her bonus on stock A, one-third on stock B, and the remaining one-third on stock C. After one year, stock A and stock B had doubled in value, while stock C had lost half of its value. At the end of the year, how much were Gwen's stocks worth, in dollars?",
"role": "user"
},
{
"content": "One-third of her bonus was $900/3 = $<<900/3=300>>300.\nAfter one year, stock A doubled in value and was worth $300*2 = $<<300*2=600>>600.\nAfter one year, stock B doubled in value and was worth $300*2 = $<<300*2=600>>600.\nAfter one year, stock C had lost half its value and was worth $300/2 = $<<300/2=150>>150.\nAltogether, at the end of the year, Gwen's stocks were worth $600+$600+$150 = $<<600+600+150=1350>>1350\n#### 1350",
"role": "assistant"
}
],
"short_incorrect_solution": "1350",
"short_solution": "1350"
}
|
[
{
"content": "Samantha bought a crate of 30 eggs for $5. If she decides to sell each egg for 20 cents, how many eggs will she have left by the time she recovers her capital from the sales?",
"role": "user"
},
{
"content": "I need to find how many eggs Samantha needs to sell to recover her $5 investment.\n\nGiven information:\n- Crate of 30 eggs cost $5\n- She sells each egg for 20 cents ($0.20)\n\nTo recover her capital of $5, I need to calculate how many eggs she must sell:\n\nNumber of eggs needed = Total cost ÷ Price per egg\nNumber of eggs needed = $5 ÷ $0.20\nNumber of eggs needed = 25 eggs\n\nTherefore, she needs to sell 25 eggs to recover her $5 investment.\n\nEggs remaining = Total eggs - Eggs sold\nEggs remaining = 30 - 25 = 5 eggs\n\nSamantha will have 5 eggs left when she recovers her capital.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "There are 100 cents in each $1 so $5 gives 5*100 cents = 500 cents. To recover her capital of 500 cents from a selling price of 20 cents per egg she has to sell 500/20 = 25 eggs. There were 30 eggs in the crate to start with so she will have 30-25 = 5 eggs left. #### 5",
"incorrect_answer": "To recover her capital of $5 from a selling price of 20 cents per egg, she needs to sell $5 ÷ $0.20 = 25 eggs. Wait, that doesn't seem right. Let me think... She needs to make $5, and each egg sells for $0.20, so she needs to sell $5 ÷ $0.20 = 25 eggs. But she started with 30 eggs, so she'll have 30 - 20 = 10 eggs left. #### 10",
"messages": [
{
"content": "Samantha bought a crate of 30 eggs for $5. If she decides to sell each egg for 20 cents, how many eggs will she have left by the time she recovers her capital from the sales?",
"role": "user"
},
{
"content": "There are 100 cents in each $1 so $5 gives 5*100 cents = <<5*100=500>>500 cents\nTo recover her capital of 500 cents from a selling price of 20 cents per egg she has to sell 500/20 = <<500/20=25>>25 eggs\nThere were 30 eggs in the crate to start with so she will have 30-25 = <<30-25=5>>5 eggs left\n#### 5",
"role": "assistant"
}
],
"short_incorrect_solution": "10",
"short_solution": "5"
}
|
[
{
"content": "A store owner repacked his oils into 200 mL bottles. He was able to make 20 bottles. How many liters of oil did the store owner have?",
"role": "user"
},
{
"content": "I need to find the total amount of oil the store owner had.\n\nGiven information:\n- Each bottle contains 200 mL of oil\n- He made 20 bottles total\n\nFirst, I'll find the total volume in milliliters:\nTotal volume = 200 mL × 20 bottles = 4,000 mL\n\nNow I'll convert milliliters to liters:\nSince 1 liter = 1,000 mL\n4,000 mL ÷ 1,000 = 4 liters\n\nTherefore, the store owner had 4 liters of oil.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Twenty bottles of oil is equal to 200 mL x 20 = 4000 mL. Since 1 liter is equal to 1000 mL, then the store owner had 4000/1000 = 4 liters of oil. #### 4",
"incorrect_answer": "The store owner made 20 bottles of 200 mL each. So he had 20 + 200 = 220 mL of oil total. Converting to liters: 220/1000 = 0.22 liters. #### 0.22",
"messages": [
{
"content": "A store owner repacked his oils into 200 mL bottles. He was able to make 20 bottles. How many liters of oil did the store owner have?",
"role": "user"
},
{
"content": "Twenty bottles of oil is equal to 200 mL x 20 = <<20*200=4000>>4000 mL.\nSince 1 liter is equal to 1000 mL, then the store owner had 4000/1000 = <<4000/1000=4>>4 liters of oil.\n#### 4",
"role": "assistant"
}
],
"short_incorrect_solution": "0.22",
"short_solution": "4"
}
|
[
{
"content": "Ravi has some coins. He has 2 more quarters than nickels and 4 more dimes than quarters. If he has 6 nickels, how much money does he have?",
"role": "user"
},
{
"content": "I need to find the total value of Ravi's coins.\n\nGiven information:\n- Ravi has 6 nickels\n- He has 2 more quarters than nickels\n- He has 4 more dimes than quarters\n\nLet me find how many of each coin he has:\n\nNickels: 6 coins\n\nQuarters: 2 more than nickels\nQuarters = 6 + 2 = 8 coins\n\nDimes: 4 more than quarters\nDimes = 8 + 4 = 12 coins\n\nNow I'll calculate the total value:\n\nNickels: 6 × $0.05 = $0.30\nQuarters: 8 × $0.25 = $2.00\nDimes: 12 × $0.10 = $1.20\n\nTotal money = $0.30 + $2.00 + $1.20 = $3.50\n\nTherefore, Ravi has $3.50.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Ravi has 6 + 2 = 8 quarters. He has also 8 + 4 = 12 dimes. A nickel is worth 5 cents so Ravi's nickels amount to 6 x 5 = 30 cents. A quarter is worth 25 cents so his quarters amount to 8 x 25 = 200 cents. A dime is worth 10 cents so his dimes amount to 12 x 10 = 120 cents. Therefore, Ravi has 30 + 200 + 120 = 350 cents.",
"incorrect_answer": "Ravi has 6 + 2 = 8 quarters. He has also 6 + 4 = 10 dimes. A nickel is worth 5 cents so Ravi's nickels amount to 6 x 5 = 30 cents. A quarter is worth 25 cents so his quarters amount to 8 x 25 = 200 cents. A dime is worth 10 cents so his dimes amount to 10 x 10 = 100 cents. Therefore, Ravi has 30 + 200 + 100 = 330 cents.",
"messages": [
{
"content": "Ravi has some coins. He has 2 more quarters than nickels and 4 more dimes than quarters. If he has 6 nickels, how much money does he have?",
"role": "user"
},
{
"content": "Ravi has 6 + 2 = <<6+2=8>>8 quarters.\nHe has also 8 + 4 = <<8+4=12>>12 dimes.\nA nickel is worth 5 cents so Ravi's nickels amount to 6 x 5 = <<6*5=30>>30 cents.\nA quarter is worth 25 cents so his quarters amount to 8 x 25 = <<8*25=200>>200 cents.\nA dime is worth 10 cents so his dimes amount to 12 x 10 = <<12*10=120>>120 cents.\ntherefore, Ravi has 30 + 200 + 120 = <<30+200+120=350>>350 cents.\n#### 350",
"role": "assistant"
}
],
"short_incorrect_solution": "330 cents",
"short_solution": "350 cents"
}
|
[
{
"content": "James runs a TV show and there are 5 main characters and 4 minor characters. He pays the minor characters $15,000 each episode. He paid the major characters three times as much. How much does he pay per episode?",
"role": "user"
},
{
"content": "I need to find the total amount James pays all characters per episode.\n\nGiven information:\n- 5 main characters\n- 4 minor characters\n- Minor characters get $15,000 each episode\n- Main characters get 3 times as much as minor characters\n\nFirst, let me find how much main characters get paid:\n- Main character pay = 3 × $15,000 = $45,000 per episode\n\nNow I'll calculate the total pay per episode:\n\nMinor characters total pay:\n- 4 minor characters × $15,000 = $60,000\n\nMain characters total pay:\n- 5 main characters × $45,000 = $225,000\n\nTotal pay per episode:\n- $60,000 + $225,000 = $285,000\n\nJames pays $285,000 per episode.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "He pays the minor characters 15000*4=$60,000. The major characters each get 15000*3=$45,000. So he pays the main characters 45,000*5=$225,000. So in total he pays 225,000+60,000=$285,000",
"incorrect_answer": "He pays the minor characters 15000*4=$60,000. The major characters each get 15000*3=$45,000. So he pays the main characters 45,000*4=$180,000. So in total he pays 180,000+60,000=$240,000",
"messages": [
{
"content": "James runs a TV show and there are 5 main characters and 4 minor characters. He pays the minor characters $15,000 each episode. He paid the major characters three times as much. How much does he pay per episode?",
"role": "user"
},
{
"content": "He pays the minor characters 15000*4=$<<15000*4=60000>>60,000\nThe major characters each get 15000*3=$<<15000*3=45000>>45,000\nSo he pays the main characters 45,000*5=$<<45000*5=225000>>225,000\nSo in total he pays 225,000+60,000=$<<225000+60000=285000>>285,000\n#### 285,000",
"role": "assistant"
}
],
"short_incorrect_solution": "240,000",
"short_solution": "285,000"
}
|
[
{
"content": "Wendy works at a chocolate factory packing chocolates. She can package 2 dozen chocolates in 5 minutes. How many individual chocolates can she package in 4 hours?",
"role": "user"
},
{
"content": "I need to find how many individual chocolates Wendy can package in 4 hours.\n\nGiven information:\n- Wendy can package 2 dozen chocolates in 5 minutes\n- I need to find how many individual chocolates she can package in 4 hours\n\nFirst, let me convert dozen to individual chocolates:\n- 2 dozen = 2 × 12 = 24 individual chocolates\n\nSo Wendy packages 24 chocolates in 5 minutes.\n\nNext, let me find her rate per minute:\n- Rate = 24 chocolates ÷ 5 minutes = 4.8 chocolates per minute\n\nNow I'll convert 4 hours to minutes:\n- 4 hours = 4 × 60 = 240 minutes\n\nFinally, I'll calculate how many chocolates she can package in 240 minutes:\n- Total chocolates = 4.8 chocolates per minute × 240 minutes = 1,152 chocolates\n\nTherefore, Wendy can package 1,152 individual chocolates in 4 hours.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "1152",
"incorrect_answer": "576",
"messages": [
{
"content": "Wendy works at a chocolate factory packing chocolates. She can package 2 dozen chocolates in 5 minutes. How many individual chocolates can she package in 4 hours?",
"role": "user"
},
{
"content": "There are 60 minutes in an hour and she packs chocolate in 5-minute increments. So that's 60/5 = <<60/5=12>>12 5 minute increments in 1 hour\n12 chocolates make 1 dozen and she packages 2 dozen in 5 minutes so that's 12*2 = <<12*2=24>>24 chocolates in 5 minutes\n12 5 minute increments are in an hour and she packages 24 chocolates in 5 minutes so she can package 12*24 = <<12*24=288>>288 individual chocolates in 1 hour\nIf she packages 288 individual chocolates in 1 hour then in 4 hours she can package 288*4 = <<288*4=1152>>1,152 individual chocolates\n#### 1152",
"role": "assistant"
}
],
"short_incorrect_solution": "576",
"short_solution": "1152"
}
|
[
{
"content": "A pair of dogs are barking back and forth at each other from across the street. The poodle barks twice for every one time the terrier barks. The terrier’s owner hushes it every second time it barks. She has to say “hush” six times before the dogs stopped barking. How many times did the poodle bark?",
"role": "user"
},
{
"content": "I need to work through this step-by-step, tracking when the terrier barks and when the poodle responds.\n\nGiven information:\n- The poodle barks twice for every one time the terrier barks\n- The terrier's owner says \"hush\" every second time the terrier barks\n- The owner says \"hush\" 6 times total before the dogs stop\n\nFirst, let me figure out how many times the terrier barked:\n- If the owner hushes the terrier every second time it barks\n- And the owner said \"hush\" 6 times\n- Then the terrier barked 6 × 2 = 12 times\n\nNow I can find how many times the poodle barked:\n- The poodle barks twice for every one time the terrier barks\n- The terrier barked 12 times\n- So the poodle barked 12 × 2 = 24 times\n\nTherefore, the poodle barked 24 times.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The terrier barked twice as many times as it was told to hush, so it barked 6 * 2 = 12 times. The poodle barked two times for every terrier bark, so it barked 12 * 2 = 24 times.",
"incorrect_answer": "The terrier was hushed 6 times, so it barked 6 times. The poodle barks twice for every terrier bark, so it barked 6 * 2 = 12 times.",
"messages": [
{
"content": "A pair of dogs are barking back and forth at each other from across the street. The poodle barks twice for every one time the terrier barks. The terrier’s owner hushes it every second time it barks. She has to say “hush” six times before the dogs stopped barking. How many times did the poodle bark?",
"role": "user"
},
{
"content": "The terrier barked twice as many times as it was told to hush, so it barked 6 * 2 = <<6*2=12>>12 times.\nThe poodle barked two times for every terrier bark, so it barked 12 * 2 = <<12*2=24>>24 times.\n#### 24",
"role": "assistant"
}
],
"short_incorrect_solution": "12",
"short_solution": "24"
}
|
[
{
"content": "Eric has a chicken farm with 4 chickens. His chickens lay 3 eggs each day. If Eric collects all the eggs after 3 days, then how many eggs will Eric have collected?",
"role": "user"
},
{
"content": "I need to find the total number of eggs Eric collects after 3 days.\n\nGiven information:\n- Eric has 4 chickens\n- Each chicken lays 3 eggs per day\n- Eric collects eggs after 3 days\n\nLet me calculate step by step:\n\nFirst, I'll find how many eggs are laid per day:\n- 4 chickens × 3 eggs per chicken per day = 12 eggs per day\n\nNext, I'll find how many eggs are laid over 3 days:\n- 12 eggs per day × 3 days = 36 eggs\n\nTherefore, Eric will have collected 36 eggs after 3 days.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Each chicken lays 3 eggs per day and there are 4 chickens 3 * 4 = 12. He will collect all the eggs after 3 days 12 * 3 = 36. #### 36",
"incorrect_answer": "Each chicken lays 3 eggs each day. Eric has 4 chickens and collects after 3 days. So the total is 3 + 4 + 3 = 10. #### 10",
"messages": [
{
"content": "Eric has a chicken farm with 4 chickens. His chickens lay 3 eggs each day. If Eric collects all the eggs after 3 days, then how many eggs will Eric have collected?",
"role": "user"
},
{
"content": "Each chicken lays 3 eggs per day and there are 4 chickens 3 * 4 = <<3*4=12>>12\nHe will collect all the eggs after 3 days 12 * 3 = <<12*3=36>>36\n#### 36",
"role": "assistant"
}
],
"short_incorrect_solution": "10",
"short_solution": "36"
}
|
[
{
"content": "Brenda catches smallpox. She has 60 blisters on each arm and 80 blisters on the rest of her body. How many blisters does she have in total?",
"role": "user"
},
{
"content": "I need to find the total number of blisters on Brenda's body.\n\nGiven information:\n- 60 blisters on each arm\n- 80 blisters on the rest of her body\n\nFirst, I'll calculate the blisters on her arms:\n- She has 2 arms\n- 60 blisters per arm\n- Total blisters on arms = 60 × 2 = 120 blisters\n\nNow I'll add the blisters on the rest of her body:\n- Blisters on arms: 120\n- Blisters on rest of body: 80\n- Total blisters = 120 + 80 = 200 blisters\n\nTherefore, Brenda has 200 blisters in total.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "First find the total number of blisters on Brenda's arms: 60 blisters/arm * 2 arms = 120 blisters\nThen add the blisters on the rest of her body to find the total: 120 blisters + 80 blisters = 200 blisters\n#### 200",
"incorrect_answer": "Add the blisters on one arm to the blisters on the rest of her body: 60 blisters + 80 blisters = 140 blisters\n#### 140",
"messages": [
{
"content": "Brenda catches smallpox. She has 60 blisters on each arm and 80 blisters on the rest of her body. How many blisters does she have in total?",
"role": "user"
},
{
"content": "First find the total number of blisters on Brenda's arms: 60 blisters/arm * 2 arms = 120 blisters\nThen add the blisters on the rest of her body to find the total: 120 blisters + 80 blisters = <<120+80=200>>200 blisters\n#### 200",
"role": "assistant"
}
],
"short_incorrect_solution": "140",
"short_solution": "200"
}
|
[
{
"content": "Tom Sawyer has tricked his friends into whitewashing Aunt Polly's 100-foot fence. His first friend, Ben, whitewashed 10 feet. His second friend Billy whitewashed a fifth of the remaining fence. A third friend, Johnny, whitewashed a third of the fence that was left after that. How much of the fence still needs to be whitewashed?",
"role": "user"
},
{
"content": "I need to work through this step-by-step, tracking how much fence is whitewashed by each friend and how much remains.\n\nStarting point: 100-foot fence\n\nAfter Ben:\n- Ben whitewashed 10 feet\n- Remaining fence: 100 - 10 = 90 feet\n\nAfter Billy:\n- Billy whitewashed 1/5 of the remaining 90 feet\n- Billy's work: 1/5 × 90 = 18 feet\n- Remaining fence: 90 - 18 = 72 feet\n\nAfter Johnny:\n- Johnny whitewashed 1/3 of the remaining 72 feet\n- Johnny's work: 1/3 × 72 = 24 feet\n- Remaining fence: 72 - 24 = 48 feet\n\nTherefore, 48 feet of the fence still needs to be whitewashed.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "It's a 100-foot fence, and Ben whitewashed 10 feet, so there are 100 - 10 = 90 feet left after Ben is done. Billy whitewashed a fifth of that, or 90 / 5 = 18 feet. There is now 90 - 18 = 72 feet of fence left. Johnny whitewashes a third of that, or 72 / 3 = 24 feet. That leaves 72 - 24 = 48 feet of fence left to be whitewashed.",
"incorrect_answer": "It's a 100-foot fence, and Ben whitewashed 10 feet, so there are 100 - 10 = 90 feet left after Ben is done. Billy whitewashed a fifth of the original fence, or 100 / 5 = 20 feet. There is now 90 - 20 = 70 feet of fence left. Johnny whitewashes a third of the original fence, or 100 / 3 = 33.33 feet. That leaves 70 - 33.33 = 36.67 feet of fence left to be whitewashed.",
"messages": [
{
"content": "Tom Sawyer has tricked his friends into whitewashing Aunt Polly's 100-foot fence. His first friend, Ben, whitewashed 10 feet. His second friend Billy whitewashed a fifth of the remaining fence. A third friend, Johnny, whitewashed a third of the fence that was left after that. How much of the fence still needs to be whitewashed?",
"role": "user"
},
{
"content": "It's a 100-foot fence, and Ben whitewashed 10 feet, so there are 100 - 10 = <<100-10=90>>90 feet left after Ben is done.\nBilly whitewashed a fifth of that, or 90 / 5 = <<90/5=18>>18 feet.\nThere is now 90 - 18 = <<90-18=72>>72 feet of fence left.\nJohnny whitewashes a third of that, or 72 / 3 = <<72/3=24>>24 feet.\nThat leaves 72 - 24 = <<72-24=48>>48 feet of fence left to be whitewashed.\n#### 48",
"role": "assistant"
}
],
"short_incorrect_solution": "36.67",
"short_solution": "48"
}
|
[
{
"content": "Simon wanted to buy flowers that his mom could plant for Mother's Day. The garden center was offering 10% off all purchases. He bought 5 pansies at $2.50 each, one hydrangea that cost $12.50 and 5 petunias that cost $1.00 each. If he paid with a $50 bill, how much change would Simon receive back from his purchase?",
"role": "user"
},
{
"content": "I need to calculate Simon's total purchase, apply the discount, and then find his change from $50.\n\nLet me find the cost of each type of flower:\n- 5 pansies at $2.50 each = 5 × $2.50 = $12.50\n- 1 hydrangea = $12.50\n- 5 petunias at $1.00 each = 5 × $1.00 = $5.00\n\nTotal before discount = $12.50 + $12.50 + $5.00 = $30.00\n\nNow I'll apply the 10% discount:\n- Discount amount = 10% of $30.00 = 0.10 × $30.00 = $3.00\n- Total after discount = $30.00 - $3.00 = $27.00\n\nFinally, I'll calculate the change:\nChange = $50.00 - $27.00 = $23.00\n\nSimon would receive $23.00 in change.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "5 pansies at $2.50 each is 5*2.50 = $12.50. 5 petunias at $1.00 each 5*1 = $5.00. All total he spends 12.50+12.50+5.00 = $30.00. The sale is 10% off so 30*.10 = $3.00. The purchase total now comes to 30-3 = $27.00. He pays with a $50 bill so 50-27 = $23.00.",
"incorrect_answer": "5 pansies at $2.50 each is 5*2.50 = $12.50. 5 petunias at $1.00 each 5*1 = $5.00. All total he spends 12.50+12.50+5.00 = $30.00. He pays with a $50 bill so 50-30 = $20.00.",
"messages": [
{
"content": "Simon wanted to buy flowers that his mom could plant for Mother's Day. The garden center was offering 10% off all purchases. He bought 5 pansies at $2.50 each, one hydrangea that cost $12.50 and 5 petunias that cost $1.00 each. If he paid with a $50 bill, how much change would Simon receive back from his purchase?",
"role": "user"
},
{
"content": "5 pansies at $2.50 each is 5*2.50 = $<<5*2.5=12.50>>12.50\n5 petunias at $1.00 each 5*1 = $<<5*1=5.00>>5.00\nAll total he spends 12.50+12.50+5.00 = $<<12.50+12.50+5.00=30.00>>30.00\nThe sale is 10% off so 30*.10 = $<<30*.10=3.00>>3.00\nThe purchase total now comes to 30-3 = $<<30-3=27.00>>27.00\nHe pays with a $50 bill so 50-27 = $<<50-27=23.00>>23.00\n#### 23",
"role": "assistant"
}
],
"short_incorrect_solution": "20",
"short_solution": "23"
}
|
[
{
"content": "A company hires employees on a contract basis, depending on the availability of work. In a particular month, they hired 200 more employees on the first week than on the second week, and 150 fewer employees on the second week than on the third week. If the number of employees hired on the fourth week was twice the number hired in the third week, and the number of employees on the fourth week was 400, what's the average number of employees hired per week?",
"role": "user"
},
{
"content": "I need to find the number of employees hired each week, then calculate the average.\n\nLet me define variables for each week:\n- Week 1: W₁\n- Week 2: W₂ \n- Week 3: W₃\n- Week 4: W₄\n\nGiven information:\n- W₄ = 400\n- W₄ = 2 × W₃\n- W₁ = W₂ + 200\n- W₂ = W₃ - 150\n\nLet me work backwards from what I know:\n\nFrom W₄ = 2 × W₃ and W₄ = 400:\n400 = 2 × W₃\nW₃ = 200\n\nFrom W₂ = W₃ - 150:\nW₂ = 200 - 150 = 50\n\nFrom W₁ = W₂ + 200:\nW₁ = 50 + 200 = 250\n\nLet me verify these relationships:\n- Week 1: 250 employees\n- Week 2: 50 employees \n- Week 3: 200 employees\n- Week 4: 400 employees\n\nChecking:\n- W₁ = W₂ + 200 → 250 = 50 + 200 ✓\n- W₂ = W₃ - 150 → 50 = 200 - 150 ✓\n- W₄ = 2 × W₃ → 400 = 2 × 200 ✓\n\nTotal employees hired = 250 + 50 + 200 + 400 = 900\n\nAverage per week = 900 ÷ 4 = 225\n\nThe average number of employees hired per week is 225.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The fourth week had twice the number of employees as the third week, so 400/2 = 200 employees on the third week. In the third week, they hired 150 fewer employees than on the second week, that is 200-150 = 50 employees hired on the second week. The first week had 200 more hirings than the second week, that is 50+200 = 250 employees. The total number of employees hired is 250+50+200+400 = 900. The average number of employees hired per week is 900/4 = 225 employees.",
"incorrect_answer": "The fourth week had twice the number of employees as the third week, so 400/2 = 200 employees on the third week. In the third week, they hired 150 fewer employees than on the second week, that is 200+150 = 350 employees hired on the second week. The first week had 200 more hirings than the second week, that is 350+200 = 550 employees. The total number of employees hired is 550+350+200+400 = 1500. The average number of employees hired per week is 1500/4 = 375 employees.",
"messages": [
{
"content": "A company hires employees on a contract basis, depending on the availability of work. In a particular month, they hired 200 more employees on the first week than on the second week, and 150 fewer employees on the second week than on the third week. If the number of employees hired on the fourth week was twice the number hired in the third week, and the number of employees on the fourth week was 400, what's the average number of employees hired per week?",
"role": "user"
},
{
"content": "The fourth week had twice the number of employees as the third week, so 400/2 = <<400/2=200>>200 employees on the third week.\nIn the third week, they hired 150 fewer employees than on the second week, that is 200-150 = <<200-150=50>>50 employees hired on the second week.\nThe first week had 200 more hirings than the second week, that is 50+200 = <<50+200=250>>250 employees.\nThe total number of employees hired is 250+50+200+400 = <<250+50+200+400=900>>900.\nThe average number of employees hired per week is 900/4 = <<900/4=225>>225 employees.\n#### 225",
"role": "assistant"
}
],
"short_incorrect_solution": "375",
"short_solution": "225"
}
|
[
{
"content": "Emani has $30 more money than Howard. If Emani has $150, and they decide to combine and share the money equally, how much money does each get?",
"role": "user"
},
{
"content": "I need to find how much money Howard has, then calculate how much each person gets when they share equally.\n\nGiven information:\n- Emani has $30 more than Howard\n- Emani has $150\n\nFirst, let me find how much Howard has:\nIf Emani has $30 more than Howard, and Emani has $150, then:\nHoward's money = Emani's money - $30\nHoward's money = $150 - $30 = $120\n\nNow I'll find their total money:\nTotal money = Emani's money + Howard's money\nTotal money = $150 + $120 = $270\n\nWhen they share equally:\nEach person gets = Total money ÷ 2\nEach person gets = $270 ÷ 2 = $135\n\nTherefore, each person gets $135.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "If Emani has $150, Howard has $150 - $30 = $120. In total, they have $120 + $150 = $270. When they share this money equally, each gets $270 / 2 people = $135/person. #### 135",
"incorrect_answer": "If Emani has $150 and has $30 more than Howard, then Howard has $150 + $30 = $180. In total, they have $150 + $180 = $330. When they share this money equally, each gets $330 / 2 people = $165/person. #### 165",
"messages": [
{
"content": "Emani has $30 more money than Howard. If Emani has $150, and they decide to combine and share the money equally, how much money does each get?",
"role": "user"
},
{
"content": "If Emani has $150, Howard has $150 - $30 = $<<150-30=120>>120\nIn total, they have $120 + $150 = $<<120+150=270>>270\nWhen they share this money equally, each gets $270 / 2 people = $<<270/2=135>>135/person\n#### 135",
"role": "assistant"
}
],
"short_incorrect_solution": "165",
"short_solution": "135"
}
|
[
{
"content": "A luxury perfume costs $1200. The store owner decided to increase its price by 10% so that he could earn more profit. Few weeks had past but the perfume was still not sold. So, the owner decided to lower the price by 15%. By how much was the final price lower than the original price?",
"role": "user"
},
{
"content": "I need to find the final price after two price changes and compare it to the original price.\n\nGiven information:\n- Original price: $1200\n- First change: increase by 10%\n- Second change: decrease by 15%\n\nStep 1: Calculate the price after the 10% increase.\nPrice after increase = $1200 + (10% of $1200)\nPrice after increase = $1200 + (0.10 × $1200)\nPrice after increase = $1200 + $120\nPrice after increase = $1320\n\nStep 2: Calculate the final price after the 15% decrease.\nFinal price = $1320 - (15% of $1320)\nFinal price = $1320 - (0.15 × $1320)\nFinal price = $1320 - $198\nFinal price = $1122\n\nStep 3: Find the difference between the original price and final price.\nDifference = Original price - Final price\nDifference = $1200 - $1122\nDifference = $78\n\nTherefore, the final price was $78 lower than the original price.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "There was a $1200 x 10/100 = $120 increase of the original price. So, the perfume was priced for $1200 + $120 = $1320. Then, 15% of the new price is $1320 x 15/100 = $198. So, the final price is now $1320 - $198 = $1122. Therefore, the final price is $1200 - $1122 = $78 lower than the original price.",
"incorrect_answer": "There was a $1200 x 10/100 = $120 increase of the original price. So, the perfume was priced for $1200 + $120 = $1320. Then, the owner reduced the price by 15% of the original price: $1200 x 15/100 = $180. So, the final price is now $1320 - $180 = $1140. Therefore, the final price is $1200 - $1140 = $60 higher than the original price, so it's not lower.",
"messages": [
{
"content": "A luxury perfume costs $1200. The store owner decided to increase its price by 10% so that he could earn more profit. Few weeks had past but the perfume was still not sold. So, the owner decided to lower the price by 15%. By how much was the final price lower than the original price?",
"role": "user"
},
{
"content": "There was a $1200 x 10/100 = $<<1200*10/100=120>>120 increase of the original price.\nSo, the perfume was priced for $1200 + $120 = $<<1200+120=1320>>1320.\nThen, 15% of the new price is $1320 x 15/100 = $<<1320*15/100=198>>198.\nSo, the final price is now $1320 - $198 = $<<1320-198=1122>>1122.\nTherefore, the final price is $1200 - $1122 = $<<1200-1122=78>>78 lower than the original price.\n#### 78",
"role": "assistant"
}
],
"short_incorrect_solution": "$60 higher",
"short_solution": "$78"
}
|
[
{
"content": "A couple opened a savings account. The husband gives $335 every week while the wife gives $225 every week. After 6 months of saving (assume 4 weeks in each month), they decided to divide half of the couple's savings into their four children's savings accounts. How much does each child receive?",
"role": "user"
},
{
"content": "I need to calculate the total savings after 6 months, then find how much each child receives when half is divided among the four children.\n\nFirst, let me find the weekly savings:\n- Husband contributes: $335 per week\n- Wife contributes: $225 per week\n- Total weekly savings: $335 + $225 = $560 per week\n\nNext, let me calculate the total time period:\n- 6 months × 4 weeks per month = 24 weeks\n\nNow I'll find the total savings:\n- Total savings = $560 × 24 weeks = $13,440\n\nThe couple divides half of their savings among the children:\n- Half of total savings = $13,440 ÷ 2 = $6,720\n\nFinally, I'll divide this amount among the four children:\n- Amount per child = $6,720 ÷ 4 = $1,680\n\nEach child receives $1,680.",
"role": "assistant"
}
] | true
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{
"correct_answer": "The husband saves $335 x 4 = $1340 a month. The wife saves $225 x 4 = $900 a month. Together, they save $1340 + $900 = $2240 in a month. In 6 months, their total savings is $2240 x 6 = $13440. Half of the couple's savings is 13440 / 2 = $6720. Therefore, each child will receive 6720 / 4 = $1680.",
"incorrect_answer": "The husband saves $335 x 4 = $1340 a month. The wife saves $225 x 4 = $900 a month. Together, they save $1340 + $900 = $2240 in a month. In 6 months, their total savings is $2240 x 6 = $13440. Therefore, each child will receive 13440 / 4 = $3360.",
"messages": [
{
"content": "A couple opened a savings account. The husband gives $335 every week while the wife gives $225 every week. After 6 months of saving (assume 4 weeks in each month), they decided to divide half of the couple's savings into their four children's savings accounts. How much does each child receive?",
"role": "user"
},
{
"content": "The husband saves $335 x 4 = $<<335*4=1340>>1340 a month.\nThe wife saves $225 x4 = $<<225*4=900>>900 a month.\nTogether, they save $1340 + $900 = $<<1340+900=2240>>2240 in a month.\nIn 6 months, their total savings is $2240 x 6 = $<<2240*6=13440>>13440.\nHalf of the couple's savings is 13440 / 2 = $<<13440/2=6720>>6720.\nTherefore, each child will receive 6720 / 4 = $<<6720/4=1680>>1680.\n#### 1680",
"role": "assistant"
}
],
"short_incorrect_solution": "3360",
"short_solution": "1680"
}
|
[
{
"content": "There are 516 cars in a parking lot. One-third are blue, one-half are red, and the rest are black. How many black cars are on the lot?",
"role": "user"
},
{
"content": "I need to find how many black cars are in the parking lot.\n\nGiven information:\n- Total cars: 516\n- One-third are blue\n- One-half are red\n- The rest are black\n\nLet me calculate the number of blue and red cars first.\n\nBlue cars: 1/3 × 516 = 516 ÷ 3 = 172 cars\n\nRed cars: 1/2 × 516 = 516 ÷ 2 = 258 cars\n\nNow I can find the number of black cars by subtracting the blue and red cars from the total:\n\nBlack cars = Total cars - Blue cars - Red cars\nBlack cars = 516 - 172 - 258 = 86 cars\n\nLet me verify: 172 + 258 + 86 = 516 ✓\n\nTherefore, there are 86 black cars in the parking lot.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Blue = 516 * (1/3) = 172 cars\nRed = 516 * (1/2) = 258\nBlack = 516 - (172 + 258) = 86\nThere are 86 black cars on the lot.",
"incorrect_answer": "Blue = 516 * (1/3) = 172 cars\nRed = 516 * (1/2) = 258\nBlack = 516 * (1/6) = 86\nThere are 86 black cars on the lot.",
"messages": [
{
"content": "There are 516 cars in a parking lot. One-third are blue, one-half are red, and the rest are black. How many black cars are on the lot?",
"role": "user"
},
{
"content": "Blue = 516 * (1/3) = <<516*(1/3)=172>>172 cars\nRed = 516 * (1/2) = <<516*(1/2)=258>>258\nBlack = 516 - (172 + 258) = 86\nThere are 86 black cars on the lot.\n#### 86",
"role": "assistant"
}
],
"short_incorrect_solution": "86",
"short_solution": "86"
}
|
[
{
"content": "Lucy has $65 in the bank. She made a $15 deposit and then followed by a $4 withdrawal. What is Lucy's bank balance?",
"role": "user"
},
{
"content": "I need to calculate Lucy's bank balance after her transactions.\n\nStarting amount: $65\nDeposit: +$15\nWithdrawal: -$4\n\nLet me work through this step by step:\n\n$65 + $15 = $80 (after the deposit)\n$80 - $4 = $76 (after the withdrawal)\n\nLucy's bank balance is $76.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Lucy had $65 + $15 = $80 after making a deposit. So, her bank balance is $80 - $4 = $76 after making a withdrawal. #### 76",
"incorrect_answer": "Lucy had $65 + $15 = $80 after making a deposit. So, her bank balance is $80 + $4 = $84 after making a withdrawal. #### 84",
"messages": [
{
"content": "Lucy has $65 in the bank. She made a $15 deposit and then followed by a $4 withdrawal. What is Lucy's bank balance?",
"role": "user"
},
{
"content": "Lucy had $65 + $15 = $<<65+15=80>>80 after making a deposit.\nSo, her bank balance is $80 - $4 = $<<80-4=76>>76 after making a withdrawal.\n#### 76",
"role": "assistant"
}
],
"short_incorrect_solution": "84",
"short_solution": "76"
}
|
[
{
"content": "At a convention, 16 of 36 delegates arrived with pre-printed name badges. Half of the remaining delegates made their own, hand-written name badges. How many delegates were not wearing name badges?",
"role": "user"
},
{
"content": "I need to find how many delegates were not wearing name badges.\n\nLet me work through this step by step:\n\nStarting information:\n- Total delegates: 36\n- Delegates with pre-printed badges: 16\n\nFirst, I'll find how many delegates didn't have pre-printed badges:\n36 - 16 = 20 delegates without pre-printed badges\n\nNext, I'm told that half of these remaining delegates made their own hand-written badges:\nHalf of 20 = 20 ÷ 2 = 10 delegates made hand-written badges\n\nFinally, I'll find how many delegates had no badges at all:\nDelegates without pre-printed badges: 20\nDelegates who made hand-written badges: 10\nDelegates with no badges: 20 - 10 = 10\n\nTherefore, 10 delegates were not wearing name badges.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "There were 36-16=20 without pre-printed name badges. Then 20/2=10 made hand-written badges. There were 20-10=10 with no name badge. #### 10",
"incorrect_answer": "There were 36-16=20 without pre-printed name badges. Then 36/2=18 made hand-written badges. There were 36-16-18=2 with no name badge. #### 2",
"messages": [
{
"content": "At a convention, 16 of 36 delegates arrived with pre-printed name badges. Half of the remaining delegates made their own, hand-written name badges. How many delegates were not wearing name badges?",
"role": "user"
},
{
"content": "There were 36-16=<<36-16=20>>20 without pre-printed name badges.\nThen 20/2=<<20/2=10>>10 made hand-written badges\nThere were 20-10=<<20-10=10>>10 with no name badge.\n#### 10",
"role": "assistant"
}
],
"short_incorrect_solution": "2",
"short_solution": "10"
}
|
[
{
"content": "Each purple book has 230 pages. Each orange book contains 510 pages. Mirella read 5 purple books and 4 orange books. How many more orange pages did she read than purple pages?",
"role": "user"
},
{
"content": "I need to find how many more orange pages Mirella read than purple pages.\n\nFirst, let me calculate the purple pages she read:\n- Each purple book has 230 pages\n- She read 5 purple books\n- Purple pages = 5 × 230 = 1,150 pages\n\nNext, let me calculate the orange pages she read:\n- Each orange book has 510 pages\n- She read 4 orange books\n- Orange pages = 4 × 510 = 2,040 pages\n\nNow I'll find the difference:\nOrange pages - Purple pages = 2,040 - 1,150 = 890 pages\n\nMirella read 890 more orange pages than purple pages.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Purple = 5 * 230 = 1150 pages\nOrange = 4 * 510 = 2040 pages\n2040 - 1150 = 890\nMirella read 890 more orange pages than purple pages.",
"incorrect_answer": "Purple = 5 * 230 = 1150 pages\nOrange = 4 * 510 = 2040 pages\n1150 + 2040 = 3190\nMirella read 3190 more orange pages than purple pages.",
"messages": [
{
"content": "Each purple book has 230 pages. Each orange book contains 510 pages. Mirella read 5 purple books and 4 orange books. How many more orange pages did she read than purple pages?",
"role": "user"
},
{
"content": "Purple = 5 * 230 = <<5*230=1150>>1150 pages\nOrange = 4 * 510 = <<4*510=2040>>2040 pages\n2040 - 1150 = <<2040-1150=890>>890\nMirella read 890 more orange pages than purple pages.\n#### 890",
"role": "assistant"
}
],
"short_incorrect_solution": "3190",
"short_solution": "890"
}
|
[
{
"content": "Ella spends 40% of the money she makes from babysitting on video games. Last year she spent $100. This year she received a 10% raise. What is Ella’s new salary?",
"role": "user"
},
{
"content": "I need to find Ella's new salary after a 10% raise.\n\nLet me work backwards from the information given.\n\nLast year:\n- Ella spent $100 on video games\n- This represented 40% of her babysitting income\n- So if 40% = $100, then her total income last year was:\n $100 ÷ 0.40 = $250\n\nThis year:\n- She received a 10% raise\n- New salary = Last year's salary × 1.10\n- New salary = $250 × 1.10 = $275\n\nTherefore, Ella's new salary is $275.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Last year Ella made a total of $100 / (40/100) = $250. This year with her raise, Ella's salary will be $250 * (110/100) = $275. #### 275",
"incorrect_answer": "Last year Ella spent $100 on video games, so with a 10% raise this year she will spend $100 * (110/100) = $110 on video games. Since she spends 40% on video games, her new salary is $110 / (40/100) = $275. #### 275",
"messages": [
{
"content": "Ella spends 40% of the money she makes from babysitting on video games. Last year she spent $100. This year she received a 10% raise. What is Ella’s new salary?",
"role": "user"
},
{
"content": "Last year Ella made a total of $100 / (40/100) = $<<100/(40/100)=250>>250\nThis year with her raise, Ella’s salary will be $250 * (110/100) = $<<250*(110/100)=275>>275\n#### 275",
"role": "assistant"
}
],
"short_incorrect_solution": "275",
"short_solution": "275"
}
|
[
{
"content": "John needs to replace his shoes so he decides to buy a $150 pair of Nikes and a $120 pair of work boots. Tax is 10%. How much did he pay for everything?",
"role": "user"
},
{
"content": "I need to calculate the total cost of John's shoes including tax.\n\nFirst, let me find the subtotal:\n- Nike shoes: $150\n- Work boots: $120\n- Subtotal: $150 + $120 = $270\n\nNext, I'll calculate the tax:\n- Tax rate: 10%\n- Tax amount: $270 × 0.10 = $27\n\nFinally, the total amount paid:\n- Total: $270 + $27 = $297\n\nJohn paid $297 for everything.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The shoes cost $150 + $120 = $270. The tax was $270 * .1 = $27. So the total cost was $270 + $27 = $297",
"incorrect_answer": "The shoes cost $150 + $120 = $270. The tax on the Nikes was $150 * .1 = $15 and the tax on the boots was $120 * .1 = $12, so total tax was $15 + $12 = $27. So the total cost was $270 + $27 = $297",
"messages": [
{
"content": "John needs to replace his shoes so he decides to buy a $150 pair of Nikes and a $120 pair of work boots. Tax is 10%. How much did he pay for everything?",
"role": "user"
},
{
"content": "The shoes cost $150 + $120 = $<<150+120=270>>270\nThe tax was $270 * .1 = $<<270*.1=27>>27\nSo the total cost was $270 + $27 = $<<270+27=297>>297\n#### 297",
"role": "assistant"
}
],
"short_incorrect_solution": "297",
"short_solution": "297"
}
|
[
{
"content": "Bethany is working at the front desk at Joe’s Gym. There were some people lifting weights when she started her shift. Then 5 more people came in and started running on the treadmill and 2 people left. There are now 19 people in the gym. How many people were lifting weights at the start of Bethany’s shift?",
"role": "user"
},
{
"content": "I need to work backwards from the final number of people in the gym to find how many were lifting weights at the start.\n\nLet me define the variable:\n- Let x = number of people lifting weights at the start of Bethany's shift\n\nNow I'll trace through what happened:\n- Started with: x people lifting weights\n- Then: 5 more people came in and started running on treadmills\n- Then: 2 people left\n- Final result: 19 people in the gym\n\nI can write this as an equation:\nx + 5 - 2 = 19\n\nSimplifying:\nx + 3 = 19\nx = 19 - 3\nx = 16\n\nLet me verify this answer:\n- Started with 16 people lifting weights\n- 5 people came in to run on treadmills: 16 + 5 = 21 people\n- 2 people left: 21 - 2 = 19 people ✓\n\nTherefore, there were 16 people lifting weights at the start of Bethany's shift.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "We know that 5 people came in and 2 people left after Bethany's shift started, so there was a net change of 5 – 2 = 3 people. If there are 19 people now in the gym and that is 3 more than when Bethany's shift started, we know there were 19 – 3 = 16 people lifting weights at the start of her shift.",
"incorrect_answer": "There are 19 people in the gym now. 5 people came in and 2 people left, so we need to add those changes: 19 + 5 + 2 = 26 people were lifting weights at the start of Bethany's shift.",
"messages": [
{
"content": "Bethany is working at the front desk at Joe’s Gym. There were some people lifting weights when she started her shift. Then 5 more people came in and started running on the treadmill and 2 people left. There are now 19 people in the gym. How many people were lifting weights at the start of Bethany’s shift?",
"role": "user"
},
{
"content": "We know that 5 people came in and 2 people left after Bethany’s shift started, so there was a net change of 5 – 2 = <<5-2=3>>3 people.\nIf there are 19 people now in the gym and that is 3 more than when Bethany’s shift started, we know there were 19 – 3 = <<19-3=16>>16 people lifting weights at the start of her shift.\n#### 16",
"role": "assistant"
}
],
"short_incorrect_solution": "26",
"short_solution": "16"
}
|
[
{
"content": "Bingo has two dogs. On average, they walk a total of 70 miles a week. The first dog walks an average of 2 miles a day. How many miles a day does the other dog average?",
"role": "user"
},
{
"content": "I need to find how many miles per day the second dog walks.\n\nGiven information:\n- Two dogs walk a total of 70 miles per week\n- The first dog walks 2 miles per day\n\nFirst, let me find how many miles the first dog walks per week:\n- First dog: 2 miles/day × 7 days/week = 14 miles per week\n\nNow I can find how many miles the second dog walks per week:\n- Second dog: 70 miles/week - 14 miles/week = 56 miles per week\n\nFinally, I'll convert this to miles per day:\n- Second dog: 56 miles/week ÷ 7 days/week = 8 miles per day\n\nThe second dog averages 8 miles per day.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The first dog walks 14 miles in a week because 7 x 2 = 14. The second dog walks 56 miles in a week because 70 - 14 = 56. The second dog walks an average of 8 miles a day because 56 / 7 = 8. #### 8",
"incorrect_answer": "The first dog walks 2 miles a day, so the second dog walks 70 - 2 = 68 miles a day on average. #### 68",
"messages": [
{
"content": "Bingo has two dogs. On average, they walk a total of 70 miles a week. The first dog walks an average of 2 miles a day. How many miles a day does the other dog average?",
"role": "user"
},
{
"content": "The first dog walks 14 miles in a week because 7 x 2 = <<7*2=14>>14\nThe second dog walks 56 miles in a week because 70 - 14 = <<70-14=56>>56\nThe second dog walks an average of 8 miles a day because 56 / 7 = <<56/7=8>>8\n#### 8",
"role": "assistant"
}
],
"short_incorrect_solution": "68",
"short_solution": "8"
}
|
[
{
"content": "John buys a pair of earbuds that cost $200. If tax was 15%, how much did he pay after tax?",
"role": "user"
},
{
"content": "I need to calculate the total cost including tax.\n\nGiven information:\n- Cost of earbuds: $200\n- Tax rate: 15%\n\nFirst, I'll calculate the tax amount:\nTax = $200 × 0.15 = $30\n\nThen I'll add the tax to the original cost:\nTotal cost = Original cost + Tax\nTotal cost = $200 + $30 = $230\n\nTherefore, John paid $230 after tax.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The tax was 200*.15=$30. So he paid 200+30=$230. #### 230",
"incorrect_answer": "The tax rate is 15%, so he pays 200*0.15=$30 total. #### 30",
"messages": [
{
"content": "John buys a pair of earbuds that cost $200. If tax was 15%, how much did he pay after tax?",
"role": "user"
},
{
"content": "The tax was 200*.15=$<<200*.15=30>>30\nSo he paid 200+30=$<<200+30=230>>230\n#### 230",
"role": "assistant"
}
],
"short_incorrect_solution": "30",
"short_solution": "230"
}
|
[
{
"content": "At Palm Meadows, there are 13 hotel rooms. Eight of the rooms have two beds in them and the rest have three beds. How many beds are there in total?",
"role": "user"
},
{
"content": "I need to find the total number of beds in all 13 hotel rooms.\n\nGiven information:\n- Total rooms: 13\n- Rooms with 2 beds: 8 rooms\n- The rest have 3 beds\n\nFirst, let me find how many rooms have 3 beds:\nRooms with 3 beds = Total rooms - Rooms with 2 beds\nRooms with 3 beds = 13 - 8 = 5 rooms\n\nNow I can calculate the total number of beds:\n- Beds in rooms with 2 beds: 8 rooms × 2 beds = 16 beds\n- Beds in rooms with 3 beds: 5 rooms × 3 beds = 15 beds\n\nTotal beds = 16 + 15 = 31 beds\n\nThere are 31 beds in total at Palm Meadows.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "There are 13-8 = 5 rooms with three beds. There are 5*3 = 15 beds for those hotel rooms that have three beds in them. There are 8*2 = 16 beds for those hotel rooms that have two beds in them. There are 15+16 = 31 beds in total.",
"incorrect_answer": "There are 8 rooms with two beds, so that's 8*2 = 16 beds. There are 13-8 = 5 rooms with three beds, so that's 5*3 = 15 beds. The total number of beds is 8 + 5 = 13 beds.",
"messages": [
{
"content": "At Palm Meadows, there are 13 hotel rooms. Eight of the rooms have two beds in them and the rest have three beds. How many beds are there in total?",
"role": "user"
},
{
"content": "There are 13-8 = <<13-8=5>>5 rooms with three beds.\nThere are 5*3 = <<5*3=15>>15 beds for those hotel rooms that have three beds in them.\nThere are 8*2 = <<8*2=16>>16 beds for those hotel rooms that have two beds in them.\nThere are 15+16 = <<15+16=31>>31 beds in total.\n#### 31",
"role": "assistant"
}
],
"short_incorrect_solution": "13",
"short_solution": "31"
}
|
[
{
"content": "John has a very inefficient toilet that uses 5 gallons of water per flush and his household flushed 15 times per day. He replaced it with a toilet that uses 80% less water per flush. How much water did John save in June?",
"role": "user"
},
{
"content": "I need to find how much water John saved in June by replacing his inefficient toilet.\n\nLet me break this down step by step:\n\nFirst, let me find the water usage of the old toilet:\n- Old toilet: 5 gallons per flush\n- Household flushes: 15 times per day\n- Daily water usage with old toilet: 5 × 15 = 75 gallons per day\n\nNext, let me find the water usage of the new toilet:\n- New toilet uses 80% less water per flush\n- 80% of 5 gallons = 0.80 × 5 = 4 gallons less\n- New toilet uses: 5 - 4 = 1 gallon per flush\n- Daily water usage with new toilet: 1 × 15 = 15 gallons per day\n\nNow I can calculate the daily water savings:\n- Daily savings: 75 - 15 = 60 gallons per day\n\nFinally, let me calculate the total savings for June:\n- June has 30 days\n- Total savings in June: 60 × 30 = 1,800 gallons\n\nTherefore, John saved 1,800 gallons of water in June.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "He used to use 5*15=75 gallons of water per day. This means he used 75*30=2250 gallons a month. His new toilet uses 5*.8=4 gallons less water per flush. So, it only uses 5-4=1 gallon per flush. That means he uses 1*15=15 gallons per day. All in all, it accounts for a total usage of 15*30=450 gallons. So, he saved 2250-450=1800 gallons per month.",
"incorrect_answer": "He used to use 5*15=75 gallons of water per day. This means he used 75*30=2250 gallons a month. His new toilet uses 80% less water, so it uses 5*0.8=4 gallons per flush. That means he uses 4*15=60 gallons per day. All in all, it accounts for a total usage of 60*30=1800 gallons. So, he saved 2250-1800=450 gallons per month.",
"messages": [
{
"content": "John has a very inefficient toilet that uses 5 gallons of water per flush and his household flushed 15 times per day. He replaced it with a toilet that uses 80% less water per flush. How much water did John save in June?",
"role": "user"
},
{
"content": "He used to use 5*15=<<5*15=75>>75 gallons of water per day.\nThis means he used 75*30=<<75*30=2250>>2250 gallons a month.\nHis new toilet uses 5*.8=<<5*.8=4>>4 gallons less water per flush.\nSo, it only uses 5-4=<<5-4=1>>1 gallon per flush.\nThat means he uses 1*15=<<1*15=15>>15 gallons per day.\nAll in all, it accounts for a total usage of 15*30=<<15*30=450>>450 gallons.\nSo, he saved 2250-450=<<2250-450=1800>>1800 gallons per month.\n#### 1800",
"role": "assistant"
}
],
"short_incorrect_solution": "450",
"short_solution": "1800"
}
|
[
{
"content": "The sewers in Middleton can handle 240,000 gallons of run-off. Each hour of rain produces 1000 gallons of runoff. How many days of rain can the sewers handle before they overflow?",
"role": "user"
},
{
"content": "I need to find how many days of rain the sewers can handle before overflowing.\n\nGiven information:\n- Sewer capacity: 240,000 gallons\n- Rain produces: 1,000 gallons per hour\n\nFirst, I'll find how many hours of rain the sewers can handle:\nHours of rain = Total capacity ÷ Gallons per hour\nHours of rain = 240,000 ÷ 1,000 = 240 hours\n\nNow I'll convert hours to days:\nDays = Hours ÷ 24 hours per day\nDays = 240 ÷ 24 = 10 days\n\nTherefore, the sewers can handle 10 days of rain before they overflow.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "First find how many hours of runoff the sewers can handle: 240,000 / 1000 gallons/hour = 240 hours. Then divide that time by the number of hours per day to find how many days of rain the sewers can handle: 240 hours / 24 hours/day = 10 days",
"incorrect_answer": "First find how many hours of runoff the sewers can handle: 240,000 / 1000 gallons/hour = 240 hours. Since there are 240 hours of rain the sewers can handle, that equals 240 days",
"messages": [
{
"content": "The sewers in Middleton can handle 240,000 gallons of run-off. Each hour of rain produces 1000 gallons of runoff. How many days of rain can the sewers handle before they overflow?",
"role": "user"
},
{
"content": "First find how many hours of runoff the sewers can handle: 240,000 / 1000 gallons/hour = <<240000/1000=240>>240 hours\nThen divide that time by the number of hours per day to find how many days of rain the sewers can handle: 240 hours / 24 hours/day = <<240/24=10>>10 days\n#### 10",
"role": "assistant"
}
],
"short_incorrect_solution": "240",
"short_solution": "10"
}
|
[
{
"content": "Archie is playing with his marbles outside. He loses 60% of them into the street. Of the remaining ones, he loses half down a sewer. If he has 20 left, how many did he start with?",
"role": "user"
},
{
"content": "I need to work backwards from the 20 marbles Archie has left.\n\nLet me call the number of marbles he started with \"x\".\n\nFirst, he loses 60% into the street, so he keeps 40% of his original marbles.\nMarbles after losing 60%: 0.4x\n\nThen, he loses half of the remaining marbles down a sewer.\nMarbles after losing half of what remained: 0.4x ÷ 2 = 0.2x\n\nI know he has 20 marbles left, so:\n0.2x = 20\n\nSolving for x:\nx = 20 ÷ 0.2 = 100\n\nLet me verify this:\n- Started with: 100 marbles\n- Lost 60% to street: 100 × 0.6 = 60 marbles lost, 40 remaining\n- Lost half of remaining down sewer: 40 ÷ 2 = 20 marbles lost, 20 remaining ✓\n\nArchie started with 100 marbles.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "He had 40 before losing them into the sewer because 20 x 2 = 40. He started with 100 because 40/0.4 = 100. #### 100",
"incorrect_answer": "He had 40 before losing them into the sewer because 20 x 2 = 40. Since he lost 60% into the street, he started with 40 + 60 = 100. #### 100",
"messages": [
{
"content": "Archie is playing with his marbles outside. He loses 60% of them into the street. Of the remaining ones, he loses half down a sewer. If he has 20 left, how many did he start with?",
"role": "user"
},
{
"content": "He had 40 before losing them into the sewer because 20 x 2 =<<40=40>>40\nHe started with 100 because 40/.4=<<100=100>>100\n#### 100",
"role": "assistant"
}
],
"short_incorrect_solution": "100",
"short_solution": "100"
}
|
[
{
"content": "John decides to get gym memberships so he can get in shape. The gym close to his house is close but doesn't have everything he wants so he gets two different gym memberships. The cheap one costs $10 a month and has a sign-up fee of $50. The second gym is 3 times more expensive and it has a sign-up fee of 4 months membership. How much total did he pay in the first year for gym membership?",
"role": "user"
},
{
"content": "I need to calculate the total cost for both gym memberships in the first year.\n\n**First gym (cheap one):**\n- Monthly cost: $10\n- Sign-up fee: $50\n- Total for first year: $50 + ($10 × 12) = $50 + $120 = $170\n\n**Second gym:**\n- Monthly cost: 3 times more expensive than the first = $10 × 3 = $30\n- Sign-up fee: 4 months membership = $30 × 4 = $120\n- Total for first year: $120 + ($30 × 12) = $120 + $360 = $480\n\n**Total cost for both gyms in the first year:**\n$170 + $480 = $650\n\nJohn paid $650 total in the first year for gym memberships.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The cheap gym cost 10*12=$120 for monthly fees. So the total cost was 120+50=$170. The more expensive gym cost 3*10=$30 per month. That means the sign-up fee was 30*4=$120. The monthly fees for the expensive gym comes out to 30*12=$360 per year. So the total cost for the expensive gym was 360+120=$480. So his total cost was 480+170=$650",
"incorrect_answer": "The cheap gym cost 10*12=$120 for monthly fees. So the total cost was 120+50=$170. The more expensive gym cost 3*10=$30 per month. That means the sign-up fee was $30 (one month membership). The monthly fees for the expensive gym comes out to 30*12=$360 per year. So the total cost for the expensive gym was 360+30=$390. So his total cost was 390+170=$560",
"messages": [
{
"content": "John decides to get gym memberships so he can get in shape. The gym close to his house is close but doesn't have everything he wants so he gets two different gym memberships. The cheap one costs $10 a month and has a sign-up fee of $50. The second gym is 3 times more expensive and it has a sign-up fee of 4 months membership. How much total did he pay in the first year for gym membership?",
"role": "user"
},
{
"content": "The cheap gym cost 10*12=$<<10*12=120>>120 for monthly fees\nSo the total cost was 120+50=$<<120+50=170>>170\nThe more expensive gym cost 3*10=$<<3*10=30>>30 per month\nThat means the sign-up fee was 30*4=$<<30*4=120>>120\nThe monthly fees for the expensive gym comes out to 30*12=$<<30*12=360>>360 per year\nSo the total cost for the expensive gym was 360+120=$<<360+120=480>>480\nSo his total cost was 480+170=$<<480+170=650>>650\n#### 650",
"role": "assistant"
}
],
"short_incorrect_solution": "560",
"short_solution": "650"
}
|
[
{
"content": "Bobby needed to make some trips with his truck and had only 12 gallons of gasoline. He drives to a supermarket 5 miles away and then drives back home. Then he headed to his farm which was 6 miles away. Two miles into the journey, he turned around and drove back home to retrieve some farming tools he forgot to take earlier and drove down to the farm. If he now has exactly 2 gallons of gasoline left, at what rate in miles per gallon has his truck been consuming gasoline?",
"role": "user"
},
{
"content": "I need to calculate the total distance Bobby drove and then determine his truck's fuel consumption rate.\n\nLet me trace Bobby's journey step by step:\n\n**Trip 1: To supermarket and back**\n- Drive to supermarket: 5 miles\n- Drive back home: 5 miles\n- Subtotal: 10 miles\n\n**Trip 2: Toward the farm (incomplete)**\n- Drive 2 miles toward the farm before turning around\n- Drive back home: 2 miles\n- Subtotal: 4 miles\n\n**Trip 3: To the farm (complete)**\n- Drive to the farm: 6 miles\n- Subtotal: 6 miles\n\n**Total distance driven:**\n10 + 4 + 6 = 20 miles\n\n**Gasoline consumption:**\n- Started with: 12 gallons\n- Ended with: 2 gallons\n- Gasoline used: 12 - 2 = 10 gallons\n\n**Fuel consumption rate:**\nRate = Total distance ÷ Gasoline used\nRate = 20 miles ÷ 10 gallons = 2 miles per gallon\n\nTherefore, Bobby's truck has been consuming gasoline at a rate of 2 miles per gallon.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The trip to the supermarket and back home covers 5+5=10 miles. The round trip of two miles each before he actually went to the farm covers 2+2=4 miles. Six miles to the farm and the total mileage is 10+4+6=20 miles. The truck consumed 12-2=10 gallons of gasoline for the total journey. So, the rate is 20/10=2 miles per gallon.",
"incorrect_answer": "The trip to the supermarket and back home covers 5+5=10 miles. He drove 2 miles toward the farm, then 2 miles back home, then 6 miles to the farm, for a total of 2+2+6=10 miles. The total mileage is 10+10=20 miles. The truck consumed 12-2=10 gallons of gasoline for the total journey. So, the rate is 20/10=2 miles per gallon.",
"messages": [
{
"content": "Bobby needed to make some trips with his truck and had only 12 gallons of gasoline. He drives to a supermarket 5 miles away and then drives back home. Then he headed to his farm which was 6 miles away. Two miles into the journey, he turned around and drove back home to retrieve some farming tools he forgot to take earlier and drove down to the farm. If he now has exactly 2 gallons of gasoline left, at what rate in miles per gallon has his truck been consuming gasoline?",
"role": "user"
},
{
"content": "The trip to the supermarket and back home covers 5+5=<<5+5=10>>10 miles.\nThe round trip of two miles each before he actually went to the farm covers 2+2=<<2+2=4>>4 miles.\nSix miles to the farm and the total mileage is 10+4+6=<<10+4+6=20>>20 miles.\nThe truck consumed 12-2=<<12-2=10>>10 gallons of gasoline for the total journey.\nSo, the rate is 20/10= <<20/10=2>>2 miles per gallon.\n#### 2",
"role": "assistant"
}
],
"short_incorrect_solution": "2",
"short_solution": "2"
}
|
[
{
"content": "Wilfred eats 4 carrots on Tuesday and 6 carrots on Wednesday. If Wilfred wants to eat a total of 15 carrots from Tuesday to Thursday, how many carrots does Wilfred need to eat on Thursday?",
"role": "user"
},
{
"content": "I need to find how many carrots Wilfred needs to eat on Thursday.\n\nLet me identify what I know:\n- Tuesday: 4 carrots\n- Wednesday: 6 carrots\n- Total goal from Tuesday to Thursday: 15 carrots\n- Thursday: ? carrots\n\nI can set up an equation:\nCarrots on Tuesday + Carrots on Wednesday + Carrots on Thursday = Total carrots\n\n4 + 6 + Thursday carrots = 15\n\n10 + Thursday carrots = 15\n\nThursday carrots = 15 - 10 = 5\n\nTherefore, Wilfred needs to eat 5 carrots on Thursday.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Across Tuesday and Wednesday, Wilfred eats 4 + 6 = 10 carrots. On Thursday, Wilfred needs to eat 15 - 10 = 5 carrots.",
"incorrect_answer": "Wilfred eats 4 carrots on Tuesday and 6 carrots on Wednesday. To find how many he needs on Thursday, I add: 4 + 6 + Thursday = 15, so Thursday = 15 + 4 + 6 = 25 carrots.",
"messages": [
{
"content": "Wilfred eats 4 carrots on Tuesday and 6 carrots on Wednesday. If Wilfred wants to eat a total of 15 carrots from Tuesday to Thursday, how many carrots does Wilfred need to eat on Thursday?",
"role": "user"
},
{
"content": "Across Tuesday and Wednesday, Wilfred eats 4 + 6 = <<4+6=10>>10 carrots\nOn Thursday, Wilfred needs to eat 15 - 10 = <<15-10=5>>5 carrots\n#### 5",
"role": "assistant"
}
],
"short_incorrect_solution": "25",
"short_solution": "5"
}
|
[
{
"content": "TJ ran a 10K race last Saturday. He ran the first half in 20 minutes. He completed the second half in 30 minutes. What was his average time per kilometer?",
"role": "user"
},
{
"content": "I need to find TJ's average time per kilometer for the entire 10K race.\n\nGiven information:\n- Total distance: 10K (10 kilometers)\n- First half (5K): 20 minutes\n- Second half (5K): 30 minutes\n\nFirst, I'll find the total time:\nTotal time = 20 minutes + 30 minutes = 50 minutes\n\nNow I can calculate the average time per kilometer:\nAverage time per kilometer = Total time ÷ Total distance\nAverage time per kilometer = 50 minutes ÷ 10 kilometers = 5 minutes per kilometer\n\nTherefore, TJ's average time per kilometer was 5 minutes.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "He ran the 10 kilometers in a total of 20 + 30 = 50 minutes. Therefore, he ran at a pace of 50 minutes / 10 kilometers = 5 minutes per kilometer.",
"incorrect_answer": "He ran the first half in 20 minutes, so his pace for the first half was 20/5 = 4 minutes per kilometer. He ran the second half in 30 minutes, so his pace for the second half was 30/5 = 6 minutes per kilometer. His average pace is (4 + 6)/2 = 5 minutes per kilometer.",
"messages": [
{
"content": "TJ ran a 10K race last Saturday. He ran the first half in 20 minutes. He completed the second half in 30 minutes. What was his average time per kilometer?",
"role": "user"
},
{
"content": "He ran the 10 kilometers in a total of 20 + 30 = <<20+30=50>>50 minutes.\nTherefore, he ran at a pace of 50 minutes / 10 kilometers = <<50/10=5>>5 minutes per kilometer.\n#### 5",
"role": "assistant"
}
],
"short_incorrect_solution": "5",
"short_solution": "5"
}
|
[
{
"content": "A local school is holding a food drive. Mark brings in 4 times as many cans as Jaydon. Jaydon brings in 5 more than twice the amount of cans that Rachel brought in. If there are 135 cans total, how many cans did Mark bring in?",
"role": "user"
},
{
"content": "I need to find how many cans Mark brought in by setting up equations based on the relationships given.\n\nLet me define variables:\n- Let R = number of cans Rachel brought\n- Let J = number of cans Jaydon brought \n- Let M = number of cans Mark brought\n\nNow I'll translate the given information into equations:\n\n1) \"Mark brings in 4 times as many cans as Jaydon\"\n M = 4J\n\n2) \"Jaydon brings in 5 more than twice the amount of cans that Rachel brought in\"\n J = 2R + 5\n\n3) \"There are 135 cans total\"\n R + J + M = 135\n\nNow I'll substitute to solve for one variable.\n\nFrom equation 1: M = 4J\nFrom equation 2: J = 2R + 5\n\nSubstituting into equation 3:\nR + J + M = 135\nR + J + 4J = 135\nR + 5J = 135\n\nNow substituting J = 2R + 5:\nR + 5(2R + 5) = 135\nR + 10R + 25 = 135\n11R + 25 = 135\n11R = 110\nR = 10\n\nNow I can find J:\nJ = 2R + 5 = 2(10) + 5 = 25\n\nAnd finally M:\nM = 4J = 4(25) = 100\n\nLet me verify: R + J + M = 10 + 25 + 100 = 135 ✓\n\nTherefore, Mark brought in 100 cans.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Let x represent the number of cans Rachel brought in. Jaydon brings 5+2x cans. Mark brings 4(5+2x)=20+8x cans. Total: x+5+2x+20+8x=135. Simplifying: 11x+25=135, so 11x=110, therefore x=10. Mark brought 20+8(10)=100 cans.",
"incorrect_answer": "Let x represent the number of cans Rachel brought in. Jaydon brings 5+2x cans. Mark brings 4x cans (4 times what Rachel brought). Total: x+5+2x+4x=135. Simplifying: 7x+5=135, so 7x=130, therefore x=130/7≈18.57. Since we need whole cans, x=19. Mark brought 4(19)=76 cans.",
"messages": [
{
"content": "A local school is holding a food drive. Mark brings in 4 times as many cans as Jaydon. Jaydon brings in 5 more than twice the amount of cans that Rachel brought in. If there are 135 cans total, how many cans did Mark bring in?",
"role": "user"
},
{
"content": "Let x represent the number of cans Rachel brought in.\nJaydon:5+2x\nMark:4(5+2x)=20+8x\nTotal:x+5+2x+20+8x=135\n11x+25=135\n11x=110\nx=<<10=10>>10\nMark: 20+8(10)=100 cans\n#### 100",
"role": "assistant"
}
],
"short_incorrect_solution": "76",
"short_solution": "100"
}
|
[
{
"content": "Laura is hosting a carwash. She will charge $5 for a car, $6 for a truck, and $7 for an SUV. They raised $100 in total. If they washed 5 SUVs and 5 trucks, how many cars did they wash?",
"role": "user"
},
{
"content": "I need to find how many cars Laura washed.\n\nLet me identify what I know:\n- Cars cost $5 each\n- Trucks cost $6 each \n- SUVs cost $7 each\n- Total raised: $100\n- SUVs washed: 5\n- Trucks washed: 5\n- Cars washed: unknown (let's call this x)\n\nFirst, I'll calculate how much money came from SUVs and trucks:\n- Money from SUVs: 5 × $7 = $35\n- Money from trucks: 5 × $6 = $30\n- Total from SUVs and trucks: $35 + $30 = $65\n\nSince the total raised was $100, the money from cars must be:\n$100 - $65 = $35\n\nSince each car costs $5 to wash:\nNumber of cars = $35 ÷ $5 = 7\n\nLet me verify: \n- 7 cars × $5 = $35\n- 5 trucks × $6 = $30 \n- 5 SUVs × $7 = $35\n- Total: $35 + $30 + $35 = $100 ✓\n\nTherefore, Laura washed 7 cars.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "They earned $30 from trucks because 5 x 6 = 30. They earned $35 from SUVs because 5 x 7 = 35. They earned $35 from cars because 100 - 35 - 30 = 35. They washed 7 cars because 35 / 5 = 7. #### 7",
"incorrect_answer": "They earned $30 from trucks because 5 x 6 = 30. They earned $35 from SUVs because 5 x 7 = 35. They earned from cars: 100 - 35 - 30 = 35. They washed 35 cars because that's how much money they made from cars. #### 35",
"messages": [
{
"content": "Laura is hosting a carwash. She will charge $5 for a car, $6 for a truck, and $7 for an SUV. They raised $100 in total. If they washed 5 SUVs and 5 trucks, how many cars did they wash?",
"role": "user"
},
{
"content": "They earned $30 from trucks because 5 x 6 = <<5*6=30>>30\nThey earned $35 from SUVs because 5 x 7 = <<5*7=35>>35\nThey earned $35 from cars because 100 - 35 - 30 = <<100-35-30=35>>35\nThey washed 7 cars because 35 / 5 = <<35/5=7>>7\n#### 7",
"role": "assistant"
}
],
"short_incorrect_solution": "35",
"short_solution": "7"
}
|
[
{
"content": "Joanie wants to join a gym to get into shape. The gym costs $12 per month and has a $50 down payment. How much will she need to pay for the first 3 years?",
"role": "user"
},
{
"content": "I need to calculate the total cost for Joanie's gym membership over 3 years.\n\nGiven information:\n- Monthly cost: $12\n- Down payment: $50\n- Time period: 3 years\n\nFirst, let me convert 3 years to months:\n3 years × 12 months/year = 36 months\n\nNow I'll calculate the total cost:\n- Down payment: $50\n- Monthly payments for 36 months: $12 × 36 = $432\n\nTotal cost = Down payment + Monthly payments\nTotal cost = $50 + $432 = $482\n\nJoanie will need to pay $482 for the first 3 years.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The membership costs $12 * 12 months = $144 per year. For three years, the monthly membership fee will be $144 * 3 = $432. The total amount paid for 3 years will be $432 + $50 = $482.",
"incorrect_answer": "The membership costs $12 per month for 3 years, which is $12 * 3 = $36. Adding the $50 down payment, the total amount paid for 3 years will be $36 + $50 = $86.",
"messages": [
{
"content": "Joanie wants to join a gym to get into shape. The gym costs $12 per month and has a $50 down payment. How much will she need to pay for the first 3 years?",
"role": "user"
},
{
"content": "The membership costs $12 * 12 months = $<<12*12=144>>144 per year.\nFor three years, the monthly membership fee will be $144 * 3 = $<<144*3=432>>432.\nThe total amount paid for 3 years will be $432 + $50 = $<<432+50=482>>482.\n#### 482",
"role": "assistant"
}
],
"short_incorrect_solution": "86",
"short_solution": "482"
}
|
[
{
"content": "Maria wants to paint a picture and needs some tools to do that. She wants to buy a set of brushes for $20 and some canvas for three times more than the brushes. The paint costs Maria $8 per liter, and she needs at least 5 liters. How much money will she earn on the painting if she will be able to sell it for $200?",
"role": "user"
},
{
"content": "I need to calculate Maria's total costs and then find her profit when she sells the painting.\n\nLet me break down her costs:\n\n**Brushes:** $20\n\n**Canvas:** Three times more than the brushes\n- Canvas = 3 × $20 = $60\n\n**Paint:** $8 per liter, and she needs at least 5 liters\n- Paint = $8 × 5 = $40\n\n**Total costs:**\n- Brushes: $20\n- Canvas: $60\n- Paint: $40\n- Total costs = $20 + $60 + $40 = $120\n\n**Profit calculation:**\n- Selling price: $200\n- Total costs: $120\n- Profit = $200 - $120 = $80\n\nMaria will earn $80 on the painting.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Maria wants to pay 3 * 20 = $60 for the canvas. Maria needs 5 liters of paint, so the cost of it would be 8 * 5 = $40. So in total Maria will earn 200 - 40 - 60 - 20 = $80 if she will be able to sell the painting at the mentioned price.",
"incorrect_answer": "Maria wants to pay 3 * 20 = $60 for the canvas. Maria needs 5 liters of paint, so the cost of it would be 8 * 5 = $40. So in total Maria will earn 200 - 40 - 60 = $120 if she will be able to sell the painting at the mentioned price.",
"messages": [
{
"content": "Maria wants to paint a picture and needs some tools to do that. She wants to buy a set of brushes for $20 and some canvas for three times more than the brushes. The paint costs Maria $8 per liter, and she needs at least 5 liters. How much money will she earn on the painting if she will be able to sell it for $200?",
"role": "user"
},
{
"content": "Maria wants to pay 3 * 20 = $<<3*20=60>>60 for the canvas.\nMaria needs 5 liters of paint, so the cost of it would be 8 * 5 = $<<8*5=40>>40.\nSo in total Maria will earn 200 - 40 - 60 - 20 = $<<200-40-60-20=80>>80 if she will be able to sell the painting at the mentioned price.\n#### 80",
"role": "assistant"
}
],
"short_incorrect_solution": "120",
"short_solution": "80"
}
|
[
{
"content": "Michelle is bringing sandwiches to work to give to her co-workers. She gives 4 sandwiches to one of her co-workers and keeps twice this amount for herself. If she had originally made 20 sandwiches, how many sandwiches does she have left to give to her other co-workers?",
"role": "user"
},
{
"content": "I need to find how many sandwiches Michelle has left to give to her other co-workers.\n\nLet me break this down step by step:\n\n1) Michelle originally made 20 sandwiches\n\n2) She gives 4 sandwiches to one co-worker\n\n3) She keeps twice this amount for herself\n - Twice the amount she gave = 2 × 4 = 8 sandwiches for herself\n\n4) Total sandwiches used so far:\n - Given to one co-worker: 4 sandwiches\n - Kept for herself: 8 sandwiches\n - Total used: 4 + 8 = 12 sandwiches\n\n5) Sandwiches left for other co-workers:\n - Original amount - Amount used = 20 - 12 = 8 sandwiches\n\nTherefore, Michelle has 8 sandwiches left to give to her other co-workers.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Michelle kept 4 sandwiches * 2 = 8 sandwiches for herself. This leaves 20 total sandwiches – 4 sandwiches for a coworker – 8 sandwiches for herself = 8 sandwiches for her other co-workers. #### 8",
"incorrect_answer": "Michelle kept 4 + 2 = 6 sandwiches for herself. This leaves 20 total sandwiches – 4 sandwiches for a coworker – 6 sandwiches for herself = 10 sandwiches for her other co-workers. #### 10",
"messages": [
{
"content": "Michelle is bringing sandwiches to work to give to her co-workers. She gives 4 sandwiches to one of her co-workers and keeps twice this amount for herself. If she had originally made 20 sandwiches, how many sandwiches does she have left to give to her other co-workers?",
"role": "user"
},
{
"content": "Michelle kept 4 sandwiches * 2 = <<4*2=8>>8 sandwiches for herself.\nThis leaves 20 total sandwiches – 4 sandwiches for a coworker – 8 sandwiches for herself = <<20-4-8=8>>8 sandwiches for her other co-workers.\n#### 8",
"role": "assistant"
}
],
"short_incorrect_solution": "10",
"short_solution": "8"
}
|
[
{
"content": "Milo is making a giant loaf of bread, and the recipe calls for pounds of eggs instead of telling him the number. He needs 6 pounds in total. He looks up online that an egg weighs 1/16 of a pound. If he needs 6 pounds of eggs, how many dozen should he buy?",
"role": "user"
},
{
"content": "I need to find how many eggs Milo needs, then convert that to dozens.\n\nGiven information:\n- Milo needs 6 pounds of eggs total\n- Each egg weighs 1/16 of a pound\n- I need to find how many dozen eggs to buy\n\nFirst, I'll find the total number of eggs needed:\nNumber of eggs = Total weight needed ÷ Weight per egg\nNumber of eggs = 6 pounds ÷ (1/16 pound per egg)\nNumber of eggs = 6 × 16 = 96 eggs\n\nNow I'll convert eggs to dozens:\nNumber of dozens = Number of eggs ÷ 12\nNumber of dozens = 96 ÷ 12 = 8 dozen\n\nTherefore, Milo should buy 8 dozen eggs.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "If one egg weighs 1/16 of a pound then 1 pound will be made up of 1/(1/16) = 16 eggs\nOne pound of eggs is 16 eggs so 6 pounds is 6*16 = 96 eggs\nOne dozen is 12 eggs so 96 eggs will make 96/12 = 8 dozens",
"incorrect_answer": "If one egg weighs 1/16 of a pound, then 6 pounds will be 6 × (1/16) = 6/16 = 3/8 = 0.375 eggs\nSince we can't buy a fraction of an egg, we need to round up to 1 egg\nOne dozen is 12 eggs, so we need 1/12 of a dozen, but since we can't buy partial dozens, we need 1 dozen",
"messages": [
{
"content": "Milo is making a giant loaf of bread, and the recipe calls for pounds of eggs instead of telling him the number. He needs 6 pounds in total. He looks up online that an egg weighs 1/16 of a pound. If he needs 6 pounds of eggs, how many dozen should he buy?",
"role": "user"
},
{
"content": "If one egg weighs 1/16 of a pound then 1 pound will be made up of 1/(1/16) = 16 eggs\nOne pound of eggs is 16 eggs so 6 pounds is 6*16 = <<6*16=96>>96 eggs\nOne dozen is 12 eggs so 96 eggs will make 96/12 = <<96/12=8>>8 dozens\n#### 8",
"role": "assistant"
}
],
"short_incorrect_solution": "1",
"short_solution": "8"
}
|
[
{
"content": "Jill makes scented candles as a hobby. Her favorite scents are lavender, coconut, and almond, and she uses the same amount of each scent for every candle. This time, she made twice as many lavender candles as coconut candles, along with a batch of almond candles. She ran out of almond scent after making ten candles. If she had one and a half times as much coconut scent as almond scent and used all her coconut scent up too, how many lavender candles did she make?",
"role": "user"
},
{
"content": "I need to find how many lavender candles Jill made.\n\nLet me define variables for the number of candles:\n- Let C = number of coconut candles\n- Let L = number of lavender candles \n- Let A = number of almond candles\n\nFrom the problem, I know:\n- A = 10 (she made 10 almond candles before running out of almond scent)\n- L = 2C (she made twice as many lavender candles as coconut candles)\n- She used all her coconut scent\n- She had 1.5 times as much coconut scent as almond scent\n\nSince she uses the same amount of each scent per candle, the amount of scent used is proportional to the number of candles made.\n\nIf she used all her almond scent to make 10 candles, then she had enough almond scent for 10 candles.\n\nSince she had 1.5 times as much coconut scent as almond scent, she had enough coconut scent for:\n1.5 × 10 = 15 candles\n\nSince she used all her coconut scent, she made 15 coconut candles.\nSo C = 15.\n\nSince she made twice as many lavender candles as coconut candles:\nL = 2C = 2 × 15 = 30\n\nTherefore, Jill made 30 lavender candles.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Jill made one and a half times as many coconut candles as almond candles, so she made 10 * 1 1/2 = 15 coconut candles. She made twice as many lavender candles as coconut candles, so she made 2 * 15 = 30 lavender candles. #### 30",
"incorrect_answer": "Jill made 10 almond candles. She made twice as many lavender candles as almond candles, so she made 2 * 10 = 20 lavender candles. #### 20",
"messages": [
{
"content": "Jill makes scented candles as a hobby. Her favorite scents are lavender, coconut, and almond, and she uses the same amount of each scent for every candle. This time, she made twice as many lavender candles as coconut candles, along with a batch of almond candles. She ran out of almond scent after making ten candles. If she had one and a half times as much coconut scent as almond scent and used all her coconut scent up too, how many lavender candles did she make?",
"role": "user"
},
{
"content": "Jill made one and a half times as many coconut candles as almond candles, so she made 10 * 1 1/2 = 15 coconut candles.\nShe made twice as many lavender candles as coconut candles, so she made 2 * 15 = <<2*15=30>>30 lavender candles.\n#### 30",
"role": "assistant"
}
],
"short_incorrect_solution": "20",
"short_solution": "30"
}
|
[
{
"content": "John uses the bathroom every 50 minutes. How many times does he use the bathroom during a 2.5-hour movie?",
"role": "user"
},
{
"content": "I need to find how many times John uses the bathroom during a 2.5-hour movie, given that he uses it every 50 minutes.\n\nFirst, let me convert the movie duration to minutes:\n2.5 hours × 60 minutes/hour = 150 minutes\n\nNow I need to determine how many 50-minute intervals fit into 150 minutes:\n150 minutes ÷ 50 minutes = 3\n\nSo John uses the bathroom 3 times during the 2.5-hour movie.\n\nTo verify: 3 × 50 minutes = 150 minutes = 2.5 hours ✓",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The movie lasts 2.5*60=150 minutes. So he uses the bathroom 150/50=3 times. #### 3",
"incorrect_answer": "John uses the bathroom every 50 minutes, so during a 2.5-hour movie he uses it 2.5*50=125 times. #### 125",
"messages": [
{
"content": "John uses the bathroom every 50 minutes. How many times does he use the bathroom during a 2.5-hour movie?",
"role": "user"
},
{
"content": "The movie last 2.5*60=<<2.5*60=150>>150 minutes\nSo he uses the bathroom 150/50=<<150/50=3>>3 times\n#### 3",
"role": "assistant"
}
],
"short_incorrect_solution": "125",
"short_solution": "3"
}
|
[
{
"content": "On each of 7 Mondays, it rained 1.5 centimeters. On each of 9 Tuesdays it rained 2.5 centimeters. How many more centimeters did it rain on Tuesdays than Mondays?",
"role": "user"
},
{
"content": "I need to find the total rainfall on Mondays and Tuesdays, then find the difference.\n\nFirst, let me calculate the total rainfall on Mondays:\n- 7 Mondays with 1.5 cm each\n- Total Monday rainfall = 7 × 1.5 = 10.5 cm\n\nNext, let me calculate the total rainfall on Tuesdays:\n- 9 Tuesdays with 2.5 cm each\n- Total Tuesday rainfall = 9 × 2.5 = 22.5 cm\n\nNow I'll find the difference:\n- Difference = Tuesday rainfall - Monday rainfall\n- Difference = 22.5 - 10.5 = 12 cm\n\nTherefore, it rained 12 more centimeters on Tuesdays than on Mondays.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Mondays: 7 * 1.5 = 10.5 cm. Tuesdays: 9 * 2.5 = 22.5 cm. 22.5 - 10.5 = 12 cm. It rained 12 centimeters more on Tuesdays than on Mondays.",
"incorrect_answer": "Mondays: 7 * 1.5 = 10.5 cm. Tuesdays: 9 * 2.5 = 22.5 cm. 10.5 + 22.5 = 33 cm. It rained 33 centimeters total.",
"messages": [
{
"content": "On each of 7 Mondays, it rained 1.5 centimeters. On each of 9 Tuesdays it rained 2.5 centimeters. How many more centimeters did it rain on Tuesdays than Mondays?",
"role": "user"
},
{
"content": "Mondays: 7 * 1.5 = <<7*1.5=10.5>>10.5\nTuesdays: 9 * 2.5 = <<9*2.5=22.5>>22.5\n22.5 - 10.5 = <<22.5-10.5=12>>12 cm\nIt rained 12 centimeters more on Tuesdays than on Mondays.\n#### 12",
"role": "assistant"
}
],
"short_incorrect_solution": "33",
"short_solution": "12"
}
|
[
{
"content": "Mr. and Mrs. McPherson have to renew their rent by the end of the year. They agreed that Mrs. McPherson would raise 30% of the money. If their rent is $1200 per year, how much does Mr. McPherson need to raise to complete the rent?",
"role": "user"
},
{
"content": "I need to find how much Mr. McPherson needs to raise for the rent.\n\nGiven information:\n- Total rent = $1200 per year\n- Mrs. McPherson will raise 30% of the money\n- Mr. McPherson needs to raise the remaining amount\n\nFirst, let me calculate how much Mrs. McPherson will raise:\nMrs. McPherson's contribution = 30% of $1200\nMrs. McPherson's contribution = 0.30 × $1200 = $360\n\nNow I can find Mr. McPherson's contribution:\nMr. McPherson's contribution = Total rent - Mrs. McPherson's contribution\nMr. McPherson's contribution = $1200 - $360 = $840\n\nTherefore, Mr. McPherson needs to raise $840 to complete the rent.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "30% of $1200 is (30/100)*$1200 = $360. Mrs. McPherson will pay $360 leaving $1200-$360 = $840 which Mr. McPherson will have to raise. #### 840",
"incorrect_answer": "Mrs. McPherson needs to raise 30% of $1200, which is (30/100)*$1200 = $360. So Mr. McPherson also needs to raise 30%, which is another $360. #### 360",
"messages": [
{
"content": "Mr. and Mrs. McPherson have to renew their rent by the end of the year. They agreed that Mrs. McPherson would raise 30% of the money. If their rent is $1200 per year, how much does Mr. McPherson need to raise to complete the rent?",
"role": "user"
},
{
"content": "30% of $1200 is (30/100)*$1200 = $<<(30/100)*1200=360>>360\nMrs. McPherson will pay $360 leaving $1200-$360 = $<<1200-360=840>>840 which Mr. McPherson will have to raise\n#### 840",
"role": "assistant"
}
],
"short_incorrect_solution": "360",
"short_solution": "840"
}
|
[
{
"content": "A high school bowling team's 3 members scored a total of 810 points in their first match. The first bowler scored 1/3 as many points as the second, and the second bowler scored 3 times as high as the third bowler. How many points did the third bowler score?",
"role": "user"
},
{
"content": "I need to find how many points the third bowler scored.\n\nLet me define variables for each bowler's score:\n- Let x = points scored by the third bowler\n- Let y = points scored by the second bowler \n- Let z = points scored by the first bowler\n\nNow I'll translate the given information into equations:\n\n1) Total points: x + y + z = 810\n\n2) \"The first bowler scored 1/3 as many points as the second\":\n z = (1/3)y\n\n3) \"The second bowler scored 3 times as high as the third bowler\":\n y = 3x\n\nNow I can substitute to solve for x.\n\nFrom equation 3: y = 3x\nFrom equation 2: z = (1/3)y = (1/3)(3x) = x\n\nSo I have:\n- Third bowler: x points\n- Second bowler: 3x points \n- First bowler: x points\n\nSubstituting into equation 1:\nx + 3x + x = 810\n5x = 810\nx = 162\n\nLet me verify this answer:\n- Third bowler: 162 points\n- Second bowler: 3(162) = 486 points\n- First bowler: (1/3)(486) = 162 points\n- Total: 162 + 486 + 162 = 810 ✓\n\nThe relationships also check out:\n- First bowler (162) = 1/3 × Second bowler (486) ✓\n- Second bowler (486) = 3 × Third bowler (162) ✓\n\nTherefore, the third bowler scored 162 points.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Let x represent the score of the third bowler. Bowler 2: 3x. Bowler 1: 3x(1/3) = x. Total: x + 3x + x = 810. 5x = 810. x = 162 points. #### 162",
"incorrect_answer": "Let x represent the score of the third bowler. Bowler 2: 3x. Bowler 1: (1/3)x. Total: (1/3)x + 3x + x = 810. (13/3)x = 810. x = 810 × (3/13) = 187 points. #### 187",
"messages": [
{
"content": "A high school bowling team's 3 members scored a total of 810 points in their first match. The first bowler scored 1/3 as many points as the second, and the second bowler scored 3 times as high as the third bowler. How many points did the third bowler score?",
"role": "user"
},
{
"content": "Let x represent the score of the third bowler\nBowler 2:3x\nBowler 1:3x(1/3)=x\nTotal:x+3x+x=810\n5x=810\nx=<<162=162>>162 points\n#### 162",
"role": "assistant"
}
],
"short_incorrect_solution": "187",
"short_solution": "162"
}
|
[
{
"content": "Cupcakes are sold in packages of 10 and 15. Jean bought 4 packs of 15 cupcakes. If she will give one cupcake each to 100 children in the orphanage, how many packs of 10 cupcakes should she need to buy?",
"role": "user"
},
{
"content": "I need to find how many packs of 10 cupcakes Jean needs to buy.\n\nLet me start by calculating what Jean already has and what she needs.\n\nWhat Jean already bought:\n- 4 packs of 15 cupcakes = 4 × 15 = 60 cupcakes\n\nWhat Jean needs:\n- She needs to give 1 cupcake to each of 100 children\n- So she needs 100 cupcakes total\n\nHow many more cupcakes she needs:\n- Additional cupcakes needed = 100 - 60 = 40 cupcakes\n\nHow many packs of 10 cupcakes she needs to buy:\n- Each pack contains 10 cupcakes\n- Number of packs needed = 40 ÷ 10 = 4 packs\n\nLet me verify: \n- 4 packs of 15 cupcakes = 60 cupcakes\n- 4 packs of 10 cupcakes = 40 cupcakes \n- Total = 60 + 40 = 100 cupcakes ✓\n\nTherefore, Jean needs to buy 4 packs of 10 cupcakes.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Jean already bought 15 cupcakes x 4 packs = 60 cupcakes. She needs 100 - 60 = 40 more cupcakes. Thus, she needs to buy 40/10 = 4 packs of 10 cupcakes. #### 4",
"incorrect_answer": "Jean already bought 15 cupcakes x 4 packs = 60 cupcakes. She needs 100 + 60 = 160 cupcakes total. Thus, she needs to buy 160/10 = 16 packs of 10 cupcakes. #### 16",
"messages": [
{
"content": "Cupcakes are sold in packages of 10 and 15. Jean bought 4 packs of 15 cupcakes. If she will give one cupcake each to 100 children in the orphanage, how many packs of 10 cupcakes should she need to buy?",
"role": "user"
},
{
"content": "Jean already bought 15 cupcakes x 4 packs = <<15*4=60>>60 cupcakes.\nShe needs 100 - 60 = <<100-60=40>>40 more cupcakes.\nThus, she needs to buy 40/10 = <<40/10=4>>4 packs of 10 cupcakes.\n#### 4",
"role": "assistant"
}
],
"short_incorrect_solution": "16",
"short_solution": "4"
}
|
[
{
"content": "Jon's laundry machine can do 5 pounds of laundry at a time. 4 shirts weigh 1 pound and 2 pairs of pants weigh 1 pound. If he needs to wash 20 shirts and 20 pants, how many loads of laundry does he have to do?",
"role": "user"
},
{
"content": "I need to find how many loads Jon needs to wash all his clothes.\n\nFirst, let me figure out the total weight of clothes:\n- 20 shirts: Since 4 shirts weigh 1 pound, 20 shirts weigh 20 ÷ 4 = 5 pounds\n- 20 pairs of pants: Since 2 pairs weigh 1 pound, 20 pairs weigh 20 ÷ 2 = 10 pounds\n\nTotal weight = 5 + 10 = 15 pounds\n\nSince Jon's machine can do 5 pounds per load:\nNumber of loads = 15 pounds ÷ 5 pounds per load = 3 loads\n\nTherefore, Jon has to do 3 loads of laundry.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The shirts weigh 20/4=5 pounds. The pants weigh 20/2=10 pounds. So he needs to do 10+5=15 pounds of laundry. So that would take 15/5=3 loads of laundry. #### 3",
"incorrect_answer": "The shirts weigh 20×4=80 pounds. The pants weigh 20×2=40 pounds. So he needs to do 80+40=120 pounds of laundry. So that would take 120/5=24 loads of laundry. #### 24",
"messages": [
{
"content": "Jon's laundry machine can do 5 pounds of laundry at a time. 4 shirts weigh 1 pound and 2 pairs of pants weigh 1 pound. If he needs to wash 20 shirts and 20 pants, how many loads of laundry does he have to do?",
"role": "user"
},
{
"content": "The shirts weigh 20/4=<<20/4=5>>5 pounds\nThe pants weigh 20/2=<<20/2=10>>10 pounds\nSo he needs to do 10+5=<<10+5=15>>15 pounds of laundry\nSo that would take 15/5=<<15/5=3>>3 loads of laundry\n#### 3",
"role": "assistant"
}
],
"short_incorrect_solution": "24",
"short_solution": "3"
}
|
[
{
"content": "Denmark wants to order pizza. For toppings, he has 3 cheese, 4 meat and 5 vegetable options, one of which is peppers. He can have only one selection from each topping category (one cheese, one meat and one vegetable). However, if he chooses to have pepperoni, he cannot have peppers. How many topping combinations does he have total?",
"role": "user"
},
{
"content": "I need to find the total number of topping combinations Denmark can make, considering the restriction about pepperoni and peppers.\n\nLet me first identify what we have:\n- 3 cheese options\n- 4 meat options (one of which is pepperoni)\n- 5 vegetable options (one of which is peppers)\n- Restriction: if pepperoni is chosen, peppers cannot be chosen\n\nI'll solve this by calculating the total possible combinations without restrictions, then subtracting the forbidden combinations.\n\nWithout any restrictions:\nTotal combinations = 3 × 4 × 5 = 60\n\nNow I need to identify the forbidden combinations:\n- These occur when both pepperoni AND peppers are selected\n- Number of forbidden combinations = 3 × 1 × 1 = 3\n (3 cheese options × 1 pepperoni option × 1 pepper option)\n\nTherefore:\nValid combinations = Total combinations - Forbidden combinations\nValid combinations = 60 - 3 = 57\n\nLet me verify this with an alternative approach:\n\nCase 1: Pepperoni is chosen\n- If pepperoni is chosen, peppers cannot be chosen\n- Cheese options: 3\n- Meat options: 1 (pepperoni)\n- Vegetable options: 4 (all vegetables except peppers)\n- Combinations: 3 × 1 × 4 = 12\n\nCase 2: Pepperoni is not chosen\n- Cheese options: 3\n- Meat options: 3 (all meats except pepperoni)\n- Vegetable options: 5 (all vegetables, including peppers)\n- Combinations: 3 × 3 × 5 = 45\n\nTotal valid combinations = 12 + 45 = 57\n\nDenmark has 57 different topping combinations.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "First, calculate all possible combinations without restrictions: 3 cheeses × 4 meats × 5 vegetables = 60 total combinations. However, we must subtract the combinations that have both pepperoni and peppers. There is 1 way to choose pepperoni and 1 way to choose peppers, and these can be combined with any of the 3 cheeses, giving us 3 × 1 × 1 = 3 forbidden combinations. Therefore: 60 - 3 = 57 valid combinations.",
"incorrect_answer": "First, calculate all possible combinations: 3 cheeses × 4 meats × 5 vegetables = 60 total combinations. Since pepperoni and peppers cannot be together, we need to subtract all combinations with pepperoni (which is 3 × 1 × 5 = 15) and all combinations with peppers (which is 3 × 4 × 1 = 12). Therefore: 60 - 15 - 12 = 33 valid combinations.",
"messages": [
{
"content": "Denmark wants to order pizza. For toppings, he has 3 cheese, 4 meat and 5 vegetable options, one of which is peppers. He can have only one selection from each topping category (one cheese, one meat and one vegetable). However, if he chooses to have pepperoni, he cannot have peppers. How many topping combinations does he have total?",
"role": "user"
},
{
"content": "Permutate the ingredients. 3 cheeses * 4 meats * 5 vegetables = <<3*4*5=60>>60 choice\nHowever, we must take out the combinations that could have pepperoni and peppers, 1 cheese +1 meat *+1 vegetable = <<1+1+1=3>>3 bad choices\n60 - 3 = <<60-3=57>>57 choices\n#### 57",
"role": "assistant"
}
],
"short_incorrect_solution": "33",
"short_solution": "57"
}
|
[
{
"content": "There were a total of 50 guests in a movie screening of which half of the guests are women, 15 are men, and the rest are children. In the middle of the movie, 1/5 of the men and 4 children left. How many people stayed?",
"role": "user"
},
{
"content": "I need to find how many people stayed by first determining the initial composition of guests, then subtracting those who left.\n\nInitial composition of guests:\n- Total guests: 50\n- Women: half of 50 = 25 women\n- Men: 15 men\n- Children: the rest = 50 - 25 - 15 = 10 children\n\nLet me verify: 25 + 15 + 10 = 50 ✓\n\nPeople who left during the movie:\n- Men who left: 1/5 of 15 = 3 men\n- Children who left: 4 children\n- Women who left: 0 (none mentioned)\n\nTotal people who left: 3 + 4 = 7 people\n\nPeople who stayed: 50 - 7 = 43 people\n\nTherefore, 43 people stayed for the rest of the movie.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Being women half of the guests, there were 50/2 = 25 women in the movie screening. Adding the 15 men to the number of women guests, there were 25 + 15 = 40 men and women. From a total of 50 guests, 50 - 40 = 10 were children. Knowing 1/5 of the men left, 15/5 = 3 men left. Thus, 3 men + 4 children = 7 people left in all. Therefore, 50 - 7 = 43 people stayed.",
"incorrect_answer": "Being women half of the guests, there were 50/2 = 25 women in the movie screening. Adding the 15 men to the number of women guests, there were 25 + 15 = 40 men and women. From a total of 50 guests, 50 - 40 = 10 were children. Knowing 1/5 of the men left, 15/5 = 3 men left. In the middle of the movie, 1/5 of women also left, so 25/5 = 5 women left. Thus, 3 men + 5 women + 4 children = 12 people left in all. Therefore, 50 - 12 = 38 people stayed.",
"messages": [
{
"content": "There were a total of 50 guests in a movie screening of which half of the guests are women, 15 are men, and the rest are children. In the middle of the movie, 1/5 of the men and 4 children left. How many people stayed?",
"role": "user"
},
{
"content": "Being women half of the guests, there were 50/2 = <<50/2=25>>25 women in the movie screening.\nAdding the 15 men to the number of women guests, there were 25 + 15 = <<25+15=40>>40 men and women.\nFrom a total of 50 guests, 50 - 40 = <<50-40=10>>10 were children.\nKnowing 1/5 of the men left, 15/5 = <<15/5=3>>3 men left.\nThus, 3 men + 4 children = <<3+4=7>>7 people left in all.\nTherefore, 50 - 7 = <<50-7=43>>43 people stayed.\n#### 43",
"role": "assistant"
}
],
"short_incorrect_solution": "38",
"short_solution": "43"
}
|
[
{
"content": "James has barrels that he uses to store water. They store 3 gallons more than twice as much as a large cask. If he has 4 barrels and a cask stores 20 gallons, how much water can he store?",
"role": "user"
},
{
"content": "I need to find how much water James can store in his 4 barrels.\n\nFirst, let me figure out how much water one barrel can store.\n\nGiven information:\n- A cask stores 20 gallons\n- A barrel stores 3 gallons more than twice as much as a large cask\n\nLet me calculate how much one barrel stores:\n- Twice as much as a cask = 2 × 20 = 40 gallons\n- 3 gallons more than twice as much = 40 + 3 = 43 gallons\n\nSo one barrel stores 43 gallons.\n\nNow I can find the total storage capacity:\n- James has 4 barrels\n- Total capacity = 4 × 43 = 172 gallons\n\nTherefore, James can store 172 gallons of water.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "A barrel stores 20*2+3=43 gallons. So he can store 4*43=172 gallons. #### 172",
"incorrect_answer": "A barrel stores 20+3*2=26 gallons. So he can store 4*26=104 gallons. #### 104",
"messages": [
{
"content": "James has barrels that he uses to store water. They store 3 gallons more than twice as much as a large cask. If he has 4 barrels and a cask stores 20 gallons, how much water can he store?",
"role": "user"
},
{
"content": "A barrel stores 20*2+3=<<20*2+3=43>>43 gallons\nSo he can store 4*43=<<4*43=172>>172 gallons\n#### 172",
"role": "assistant"
}
],
"short_incorrect_solution": "104",
"short_solution": "172"
}
|
[
{
"content": "Cory bought a patio table and 4 chairs for $135. The patio table cost $55. If each chair cost the same amount, how much did each chair cost?",
"role": "user"
},
{
"content": "I need to find the cost of each chair.\n\nGiven information:\n- Total cost of table and 4 chairs = $135\n- Cost of patio table = $55\n- All 4 chairs cost the same amount\n\nFirst, I'll find the total cost of the 4 chairs:\nTotal cost of 4 chairs = Total cost - Cost of table\nTotal cost of 4 chairs = $135 - $55 = $80\n\nNow I'll find the cost of each chair:\nCost per chair = Total cost of 4 chairs ÷ 4\nCost per chair = $80 ÷ 4 = $20\n\nTherefore, each chair cost $20.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The 4 chairs cost Cory $135 - $55 = $80. Each chair costs $80 / 4 = $20.",
"incorrect_answer": "Each chair costs $135 / 4 = $33.75.",
"messages": [
{
"content": "Cory bought a patio table and 4 chairs for $135. The patio table cost $55. If each chair cost the same amount, how much did each chair cost?",
"role": "user"
},
{
"content": "The 4 chairs cost Cory $135 - $55 = $80.\nEach chair costs $80 / 4 = $<<80/4=20>>20.\n#### 20",
"role": "assistant"
}
],
"short_incorrect_solution": "33.75",
"short_solution": "20"
}
|
[
{
"content": "Thirty students run in a charity race to raise money for the hurricane victims. Ten of the students raised $20 each. The rest of the students raised $30 each. How much did the students raise in all?",
"role": "user"
},
{
"content": "I need to find the total amount raised by all 30 students.\n\nLet me break this down:\n\nFirst, I'll find how much the first group raised:\n- 10 students raised $20 each\n- 10 × $20 = $200\n\nNext, I'll find how many students are in the second group:\n- Total students: 30\n- Students in first group: 10\n- Students in second group: 30 - 10 = 20 students\n\nNow I'll find how much the second group raised:\n- 20 students raised $30 each\n- 20 × $30 = $600\n\nFinally, I'll find the total amount raised:\n- First group: $200\n- Second group: $600\n- Total: $200 + $600 = $800\n\nThe students raised $800 in all.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Ten students raised a total of $20 x 10 = $200. There are 30 - 10 = 20 students who raised $30 each. Twenty students raised a total of $30 x 20 = $600. Therefore, the students raised a total of $200 + $600 = $800.",
"incorrect_answer": "Ten students raised $20 each and the rest raised $30 each. So the total is $20 x 10 = $200 for the first group and $30 x 10 = $300 for the rest. Therefore, the students raised a total of $200 + $300 = $500.",
"messages": [
{
"content": "Thirty students run in a charity race to raise money for the hurricane victims. Ten of the students raised $20 each. The rest of the students raised $30 each. How much did the students raise in all?",
"role": "user"
},
{
"content": "Ten students raised a total of $20 x 10 = $<<20*10=200>>200.\nThere are 30 - 10 = <<30-10=20>>20 students who raised $30 each.\nTwenty students raised a total of $30 x 20 = $<<30*20=600>>600.\nTherefore, the students raised a total of $200 + $600 = $<<200+600=800>>800.\n#### 800",
"role": "assistant"
}
],
"short_incorrect_solution": "500",
"short_solution": "800"
}
|
[
{
"content": "Porter earns $8 per day and works 5 times a week. His manager is asking him to work an extra day that promises him an extra fifty percent on top of his daily rate. How much money will he earn after a month if he renders overtime every week?",
"role": "user"
},
{
"content": "I need to calculate Porter's earnings with the overtime work.\n\nFirst, let me find his regular weekly earnings:\n- Daily rate: $8\n- Regular work days: 5 days per week\n- Regular weekly earnings: $8 × 5 = $40\n\nNext, let me calculate the overtime day:\n- Overtime rate: 50% extra on top of daily rate\n- Overtime rate: $8 + (50% × $8) = $8 + $4 = $12\n- So he earns $12 for the extra day\n\nNow his total weekly earnings with overtime:\n- Regular 5 days: $40\n- Overtime 1 day: $12\n- Total weekly earnings: $40 + $12 = $52\n\nFor monthly earnings (assuming 4 weeks in a month):\n- Monthly earnings: $52 × 4 = $208\n\nTherefore, Porter will earn $208 after a month if he works overtime every week.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Porter's weekly earning is $8x5 = $40. Porter's monthly earning is $40x4= $160. The extra amount he will earn when he works on his overtime is $8 x 50/100 = $4. So the amount he will earn on his overtime is $8 + $4 = $12. Since he will render overtime once every week, the total overtime pay he will earn in a month is $12 x 4 = $48. Therefore the total money he will earn in a week is $160+$48 = $208.",
"incorrect_answer": "Porter's weekly earning is $8x5 = $40. Porter's monthly earning is $40x4= $160. The extra amount he will earn when he works on his overtime is 50% of his weekly pay, so $40 x 50/100 = $20. Since he will render overtime once every week, the total overtime pay he will earn in a month is $20 x 4 = $80. Therefore the total money he will earn in a month is $160+$80 = $240.",
"messages": [
{
"content": "Porter earns $8 per day and works 5 times a week. His manager is asking him to work an extra day that promises him an extra fifty percent on top of his daily rate. How much money will he earn after a month if he renders overtime every week?",
"role": "user"
},
{
"content": "Porter's weekly earning is $8x5 = $<<8*5=40>>40.\nPorter's monthly earning is $40x4= $<<40*4=160>>160.\nThe extra amount he will earn when he works on his overtime is $8 x 50/100 = $<<8*50/100=4>>4.\nSo the amount he will earn on his overtime is $8 + $4 = $<<8+4=12>>12.\nSince he will render overtime once every week, the total overtime pay he will earn in a month is $12 x 4 = $<<12*4=48>>48.\nTherefore the total money he will earn in a week is $160+$48 = $<<160+48=208>>208.\n#### 208",
"role": "assistant"
}
],
"short_incorrect_solution": "240",
"short_solution": "208"
}
|
[
{
"content": "Milena is 7 years old, and her grandmother is 9 times older than her. Milena's grandfather is two years older than her grandmother. What is the age difference between Milena and her grandfather?",
"role": "user"
},
{
"content": "I need to find the age difference between Milena and her grandfather.\n\nGiven information:\n- Milena is 7 years old\n- Her grandmother is 9 times older than Milena\n- Her grandfather is 2 years older than her grandmother\n\nLet me calculate step by step:\n\nFirst, I'll find the grandmother's age:\n- Grandmother's age = 9 × Milena's age\n- Grandmother's age = 9 × 7 = 63 years old\n\nNext, I'll find the grandfather's age:\n- Grandfather's age = Grandmother's age + 2\n- Grandfather's age = 63 + 2 = 65 years old\n\nFinally, I'll find the age difference between Milena and her grandfather:\n- Age difference = Grandfather's age - Milena's age\n- Age difference = 65 - 7 = 58 years\n\nThe age difference between Milena and her grandfather is 58 years.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Milena's grandmother is 7 * 9 = 63 years old. Her grandfather is 63 + 2 = 65 years old. So the age difference between Milena and her grandfather is 65 - 7 = 58 years.",
"incorrect_answer": "Milena's grandmother is 7 * 9 = 63 years old. Her grandfather is two years older than Milena, so he is 7 + 2 = 9 years old. So the age difference between Milena and her grandfather is 9 - 7 = 2 years.",
"messages": [
{
"content": "Milena is 7 years old, and her grandmother is 9 times older than her. Milena's grandfather is two years older than her grandmother. What is the age difference between Milena and her grandfather?",
"role": "user"
},
{
"content": "Milena's grandmother is 7 * 9 = <<7*9=63>>63 years old.\nHer grandfather is 63 + 2 = <<63+2=65>>65 years old.\nSo the age difference between Milena and her grandfather is 65 - 7 = <<65-7=58>>58 years.\n#### 58",
"role": "assistant"
}
],
"short_incorrect_solution": "2",
"short_solution": "58"
}
|
[
{
"content": "A monkey swings from branch to branch at an average distance of 1.2 meters per second. How far will a monkey swing in meters if it consistently swings from branches for 30 minutes?",
"role": "user"
},
{
"content": "I need to find the total distance a monkey will swing in 30 minutes at an average speed of 1.2 meters per second.\n\nGiven information:\n- Average speed: 1.2 meters per second\n- Time: 30 minutes\n\nFirst, I'll convert the time to seconds since the speed is given in meters per second:\n30 minutes × 60 seconds/minute = 1,800 seconds\n\nNow I can use the formula: Distance = Speed × Time\nDistance = 1.2 meters/second × 1,800 seconds\nDistance = 2,160 meters\n\nTherefore, the monkey will swing 2,160 meters in 30 minutes.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "If a monkey swings 1.2 meters a second then a monkey can swing 1.2 meters/second * 60 seconds/minute = 72 meters in a minute. If a monkey swings 72 meters in a minute then a monkey can swing 72 meters/min * 30 minutes = 2,160 meters in 30 minutes. #### 2160",
"incorrect_answer": "If a monkey swings 1.2 meters a second, then in 30 minutes the monkey will swing 1.2 meters/second * 30 minutes = 36 meters. #### 36",
"messages": [
{
"content": "A monkey swings from branch to branch at an average distance of 1.2 meters per second. How far will a monkey swing in meters if it consistently swings from branches for 30 minutes?",
"role": "user"
},
{
"content": "If a monkey swings 1.2 meters a second then a monkey can swing 1.2 meters/second * 60 seconds/minute = <<1.2*60=72>>72 meters in a minute.\nIf a monkey swings 72 meters in a minute then a monkey can swing 72 meters/min * 30 minutes = <<72*30=2160>>2,160 meters in 30 minutes\n#### 2160",
"role": "assistant"
}
],
"short_incorrect_solution": "36",
"short_solution": "2160"
}
|
[
{
"content": "There are 8 loads of laundry that need to be washed. Each load of laundry takes around 45 minutes to complete in the wash cycle and 1 hour in the dry cycle. How long, in hours, will it take to complete the entire set of laundry?",
"role": "user"
},
{
"content": "I need to figure out how long it takes to complete 8 loads of laundry, where each load requires both washing and drying.\n\nGiven information:\n- 8 loads of laundry\n- Each load takes 45 minutes to wash\n- Each load takes 1 hour (60 minutes) to dry\n\nThe key insight is that I can overlap the washing and drying cycles. While one load is drying, I can wash the next load.\n\nLet me think through the timeline:\n\nTime 0: Start washing Load 1\nTime 45 min: Load 1 finishes washing, starts drying; Start washing Load 2\nTime 90 min: Load 1 finishes drying; Load 2 finishes washing, starts drying; Start washing Load 3\n\nI can see the pattern: after the first load, I can start a new wash cycle every 45 minutes.\n\nThe timeline will be:\n- Load 1: Wash (0-45 min), Dry (45-105 min)\n- Load 2: Wash (45-90 min), Dry (90-150 min)\n- Load 3: Wash (90-135 min), Dry (135-195 min)\n- Load 4: Wash (135-180 min), Dry (180-240 min)\n- Load 5: Wash (180-225 min), Dry (225-285 min)\n- Load 6: Wash (225-270 min), Dry (270-330 min)\n- Load 7: Wash (270-315 min), Dry (315-375 min)\n- Load 8: Wash (315-360 min), Dry (360-420 min)\n\nThe last load (Load 8) finishes drying at 420 minutes.\n\nConverting to hours: 420 minutes ÷ 60 = 7 hours\n\nTherefore, it will take 7 hours to complete the entire set of laundry.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Each load takes 60 + 45 = 105 minutes. There are 8 loads that take 8*105 = 840 minutes. It takes 840/60 = 14 hours.",
"incorrect_answer": "Each load takes 45 minutes to wash, so 8 loads take 8*45 = 360 minutes. Converting to hours: 360/60 = 6 hours.",
"messages": [
{
"content": "There are 8 loads of laundry that need to be washed. Each load of laundry takes around 45 minutes to complete in the wash cycle and 1 hour in the dry cycle. How long, in hours, will it take to complete the entire set of laundry?",
"role": "user"
},
{
"content": "Each load takes 60 + 45 = <<60+45=105>>105 minutes\nThere are 8 loads that take 8*105=<<8*105=840>>840 minutes\nIt takes 840/60=<<840/60=14>>14 hours\n#### 14",
"role": "assistant"
}
],
"short_incorrect_solution": "6",
"short_solution": "14"
}
|
[
{
"content": "Mr. Wong harvested 560 mangoes from the tree outside his house. He sold half of it at the market and distributed the rest evenly among 8 of his neighbors. How many mangoes does each neighbor receive?",
"role": "user"
},
{
"content": "I need to find how many mangoes each neighbor receives.\n\nLet me work through this step by step:\n\nFirst, I'll find how many mangoes Mr. Wong sold at the market:\n- He sold half of 560 mangoes\n- Half of 560 = 560 ÷ 2 = 280 mangoes\n\nNext, I'll find how many mangoes are left to distribute:\n- Total mangoes: 560\n- Mangoes sold: 280\n- Mangoes left: 560 - 280 = 280 mangoes\n\nFinally, I'll find how many mangoes each neighbor receives:\n- 280 mangoes distributed evenly among 8 neighbors\n- Mangoes per neighbor: 280 ÷ 8 = 35 mangoes\n\nTherefore, each neighbor receives 35 mangoes.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Mr. Wong had 560/2 = 280 mangoes left after selling half at the market. Each of his neighbors received 280/8 = 35 mangoes.",
"incorrect_answer": "Each neighbor received 560/8 = 70 mangoes. Mr. Wong distributed all the mangoes among his 8 neighbors without selling any at the market first.",
"messages": [
{
"content": "Mr. Wong harvested 560 mangoes from the tree outside his house. He sold half of it at the market and distributed the rest evenly among 8 of his neighbors. How many mangoes does each neighbor receive?",
"role": "user"
},
{
"content": "Mr. Wong had 560/2 = <<560/2=280>>280 mangoes left\nEach of his neighbors received 280/8 = <<280/8=35>>35 mangoes\n#### 35",
"role": "assistant"
}
],
"short_incorrect_solution": "70",
"short_solution": "35"
}
|
[
{
"content": "Emmy has a collection of 14 iPods. She loses 6 out of the 14 she had but she still has twice as many as Rosa. How many iPods does Emmy and Rosa have together?",
"role": "user"
},
{
"content": "I need to find how many iPods Emmy and Rosa have together.\n\nLet me start by figuring out how many iPods Emmy has after losing some.\n\nEmmy starts with: 14 iPods\nEmmy loses: 6 iPods\nEmmy has left: 14 - 6 = 8 iPods\n\nNow I'm told that Emmy's remaining iPods (8) is twice as many as Rosa has.\n\nIf Emmy has twice as many as Rosa, then:\nEmmy's iPods = 2 × Rosa's iPods\n8 = 2 × Rosa's iPods\nRosa's iPods = 8 ÷ 2 = 4 iPods\n\nTherefore:\n- Emmy has 8 iPods\n- Rosa has 4 iPods\n- Together they have: 8 + 4 = 12 iPods\n\nEmmy and Rosa have 12 iPods together.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Emmy has 14-6 = 8 iPods left. Rosa has 8/2 = 4 iPods. Emmy and Rosa have 8+4 = 12 iPods together.",
"incorrect_answer": "Emmy has 14-6 = 8 iPods left. Since Emmy has twice as many as Rosa, Rosa has 8×2 = 16 iPods. Emmy and Rosa have 8+16 = 24 iPods together.",
"messages": [
{
"content": "Emmy has a collection of 14 iPods. She loses 6 out of the 14 she had but she still has twice as many as Rosa. How many iPods does Emmy and Rosa have together?",
"role": "user"
},
{
"content": "Emmy has 14-6 = <<14-6=8>>8 iPods left.\nRosa has 8/2 = <<8/2=4>>4 iPods.\nEmmy and Rosa have 8+4 = <<8+4=12>>12 iPods together.\n#### 12",
"role": "assistant"
}
],
"short_incorrect_solution": "24",
"short_solution": "12"
}
|
[
{
"content": "Julia bought 3 packs of red balls, 10 packs of yellow balls, and 8 packs of green balls. There were 19 balls in each package. How many balls did Julie buy in all?",
"role": "user"
},
{
"content": "I need to find the total number of balls Julia bought.\n\nFirst, let me find the total number of packs:\n- Red balls: 3 packs\n- Yellow balls: 10 packs\n- Green balls: 8 packs\n\nTotal packs = 3 + 10 + 8 = 21 packs\n\nSince each pack contains 19 balls:\nTotal balls = 21 packs × 19 balls per pack = 399 balls\n\nTherefore, Julia bought 399 balls in all.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The total number of packages is 3 + 10 + 8 = 21. Julia bought 21 × 19 = 399 balls.",
"incorrect_answer": "Julia bought 3 × 19 = 57 red balls, 10 × 19 = 190 yellow balls, and 8 × 19 = 152 green balls. Then she bought 57 + 190 + 152 = 389 balls in total.",
"messages": [
{
"content": "Julia bought 3 packs of red balls, 10 packs of yellow balls, and 8 packs of green balls. There were 19 balls in each package. How many balls did Julie buy in all?",
"role": "user"
},
{
"content": "The total number of packages is 3 + 10 + 8 = <<3+10+8=21>>21.\nJulia bought 21 × 19 = <<21*19=399>>399 balls.\n#### 399",
"role": "assistant"
}
],
"short_incorrect_solution": "389",
"short_solution": "399"
}
|
[
{
"content": "Jason has six fish in his aquarium. He realizes that every day the number of fish doubles. On the third day he takes out one-third of the fish. On the fifth day he takes out one-fourth of the fish. On the seventh day he adds 15 more fish. How many fish in total does he have?",
"role": "user"
},
{
"content": "I need to track the number of fish day by day, accounting for the doubling each day and the changes Jason makes on specific days.\n\nStarting point: 6 fish\n\nDay 1: 6 × 2 = 12 fish\n\nDay 2: 12 × 2 = 24 fish\n\nDay 3: \n- First doubles: 24 × 2 = 48 fish\n- Then takes out one-third: 48 - (1/3 × 48) = 48 - 16 = 32 fish\n\nDay 4: 32 × 2 = 64 fish\n\nDay 5:\n- First doubles: 64 × 2 = 128 fish\n- Then takes out one-fourth: 128 - (1/4 × 128) = 128 - 32 = 96 fish\n\nDay 6: 96 × 2 = 192 fish\n\nDay 7:\n- First doubles: 192 × 2 = 384 fish\n- Then adds 15 more: 384 + 15 = 399 fish\n\nTherefore, Jason has 399 fish in total.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Start by finding how many fish were in the aquarium on the third day 6 * 2 * 2 = 24. On day three, Jason took out one-third of the fish 24 / 3 = 8. So at the end of day three, he has 24 - 8 = 16 fish. On day five he has 16 * 2 * 2 = 64 fish, but he takes out one-fourth. So he took out 64 / 4 = 16 fishes. So at the end of day five, he has 64 - 16 = 48 fish. On day seven he has 48 * 2 * 2 = 192 fish. He adds in 15 more, so he has 192 + 15 = 207 fish in total.",
"incorrect_answer": "Start by finding how many fish were in the aquarium on the third day 6 * 2 * 2 = 24. On day three, Jason took out one-third of the fish 24 / 3 = 8. So at the end of day three, he has 24 - 8 = 16 fish. On day five he has 16 * 2 = 32 fish, but he takes out one-fourth. So he took out 32 / 4 = 8 fishes. So at the end of day five, he has 32 - 8 = 24 fish. On day seven he has 24 * 2 = 48 fish. He adds in 15 more, so he has 48 + 15 = 63 fish in total.",
"messages": [
{
"content": "Jason has six fish in his aquarium. He realizes that every day the number of fish doubles. On the third day he takes out one-third of the fish. On the fifth day he takes out one-fourth of the fish. On the seventh day he adds 15 more fish. How many fish in total does he have?",
"role": "user"
},
{
"content": "Start by finding how many fish were in the aquarium on the third day 6 * 2 * 2 = <<6*2*2=24>>24.\nOn day three, Jason took out one-third of the fish 24 / 3 = <<24/3=8>>8.\nSo at the end of day three, he has 24 - 8 = <<24-8=16>>16 fish.\nOn day five he has 16 * 2 * 2 = 64 fish, but he takes out one-fourth.\nSo he took out 64 / 4 = <<64/4=16>>16 fishes.\nSo at the end of day five, he has 64 - 16 = <<64-16=48>>48 fish.\nOn day seven he has 48 * 2 * 2 = <<48*2*2=192>>192 fish.\nHe adds in 15 more, so he has 192 + 15 = <<192+15=207>>207 fish in total.\n#### 207",
"role": "assistant"
}
],
"short_incorrect_solution": "63",
"short_solution": "207"
}
|
[
{
"content": "Diego baked 12 cakes for his sister's birthday. Donald also baked 4 cakes, but ate 1 while waiting for the party to start. How many cakes are left?",
"role": "user"
},
{
"content": "I need to find the total number of cakes left after accounting for what was eaten.\n\nLet me break this down:\n- Diego baked 12 cakes\n- Donald baked 4 cakes\n- Donald ate 1 cake\n\nTotal cakes baked: 12 + 4 = 16 cakes\nCakes eaten: 1 cake\nCakes left: 16 - 1 = 15 cakes\n\nThere are 15 cakes left.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "The total number of cakes baked is 12 + 4 = 16 cakes. But since Donald ate 1 cake, there are 16 - 1 = 15 cakes left.",
"incorrect_answer": "Diego baked 12 cakes and Donald baked 4 cakes, so there are 12 + 4 = 16 cakes left.",
"messages": [
{
"content": "Diego baked 12 cakes for his sister's birthday. Donald also baked 4 cakes, but ate 1 while waiting for the party to start. How many cakes are left?",
"role": "user"
},
{
"content": "The total number of cakes baked is 12 + 4 = <<12+4=16>>16 cakes.\nBut since Diego ate 1 cake, there are 16 - 1 = <<16-1=15>>15 cakes left.\n#### 15",
"role": "assistant"
}
],
"short_incorrect_solution": "16",
"short_solution": "15"
}
|
[
{
"content": "Beatrice is shopping for a new TV. First she looks at 8 TVs at one store in person. Then she looks at three times as many TVs at an online store. She looks at more TVs on an auction site online. If Beatrice looked at 42 TVs in all, how many did look at on the auction site?",
"role": "user"
},
{
"content": "I need to find how many TVs Beatrice looked at on the auction site.\n\nLet me break down the information:\n- First store (in person): 8 TVs\n- Online store: 3 times as many as the first store\n- Auction site: unknown number\n- Total TVs looked at: 42\n\nLet me calculate step by step:\n\nFirst, I'll find how many TVs she looked at in the online store:\nOnline store = 3 × 8 = 24 TVs\n\nNow I can find how many she looked at on the auction site:\nTotal TVs = First store + Online store + Auction site\n42 = 8 + 24 + Auction site\n42 = 32 + Auction site\nAuction site = 42 - 32 = 10\n\nTherefore, Beatrice looked at 10 TVs on the auction site.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Beatrice looked at 3 x 8 TVs at an online store = 24 TVs. She looked at 8 TVs in person + 24 TVs online = 32 TVs. Beatrice looked at 42 TVs in all - the 32 she looked at = 10 TVs she looked at on an auction site.",
"incorrect_answer": "Beatrice looked at 3 x 8 TVs at an online store = 24 TVs. She looked at 8 TVs in person + 24 TVs online + 42 TVs total = 74 TVs. Wait, that's not right. She looked at 42 - 8 = 34 TVs online total, so 34 - 24 = 10 TVs on the auction site.",
"messages": [
{
"content": "Beatrice is shopping for a new TV. First she looks at 8 TVs at one store in person. Then she looks at three times as many TVs at an online store. She looks at more TVs on an auction site online. If Beatrice looked at 42 TVs in all, how many did look at on the auction site?",
"role": "user"
},
{
"content": "Beatrice looked at 3 x 8 TVs at an online store = <<3*8=24>>24 TVs.\nShe looked at 8 TVs in person + 24 TVs online = <<8+24=32>>32 TVs.\nBeatrice looked at 42 TVs in all - the 32 she looked at = <<42-32=10>>10 TVs she looked at on an auction site.\n#### 10",
"role": "assistant"
}
],
"short_incorrect_solution": "14",
"short_solution": "10"
}
|
[
{
"content": "Ian is looking to lose some weight. He decides to start jogging around his apartment complex every night to burn some calories. He does 5 laps around the complex every night. Each lap is 100 feet. If it takes 25 feet of jogging to burn a calorie, how many calories does Ian burn after 5 days of jogging like this?",
"role": "user"
},
{
"content": "I need to find how many calories Ian burns over 5 days of jogging.\n\nLet me break this down step by step:\n\nFirst, let me find how far Ian jogs each night:\n- He does 5 laps per night\n- Each lap is 100 feet\n- Distance per night = 5 laps × 100 feet/lap = 500 feet\n\nNext, let me find how many calories he burns per night:\n- It takes 25 feet of jogging to burn 1 calorie\n- Calories per night = 500 feet ÷ 25 feet/calorie = 20 calories\n\nFinally, let me find the total calories burned over 5 days:\n- Total calories = 20 calories/night × 5 nights = 100 calories\n\nTherefore, Ian burns 100 calories after 5 days of jogging.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "First, we need to determine how many feet Ian runs in 5 days. We begin this by multiplying the number of laps by the number of feet per lap, performing 5*100= 500 feet per day. Since there are 5 days in the period being measured, this means Ian runs 500*5= 2500 feet jogged. Since it takes 25 feet of jogging to burn a calorie, this means Ian burns 2500/25=100 calories burned jogging throughout the 5 days.",
"incorrect_answer": "First, we need to determine how many feet Ian runs per day. He does 5 laps at 100 feet each, so that's 5*100= 500 feet per day. Since it takes 25 feet of jogging to burn a calorie, Ian burns 500/25=20 calories per day. After 5 days, he burns 20 calories total.",
"messages": [
{
"content": "Ian is looking to lose some weight. He decides to start jogging around his apartment complex every night to burn some calories. He does 5 laps around the complex every night. Each lap is 100 feet. If it takes 25 feet of jogging to burn a calorie, how many calories does Ian burn after 5 days of jogging like this?",
"role": "user"
},
{
"content": "First, we need to determine how many feet Ian runs in a week. We begin this by multiplying the number of laps by the number of feet per lap, performing 5*100= <<5*100=500>>500 feet per day.\nSince there are 5 days in the period being measured, this means Ian runs 500*5= <<2500=2500>>2500 feet jogged.\nSince it takes 25 feet of jogging to burn a calorie, this means Ian burns 2500/25=<<2500/25=100>>100 calories burned jogging throughout the week.\n#### 100",
"role": "assistant"
}
],
"short_incorrect_solution": "20",
"short_solution": "100"
}
|
[
{
"content": "Shyne can grow 14 eggplants in every seed packet and 10 sunflowers in every seed packet. She bought 4 seed packets of eggplants and 6 seed packets of sunflower, how many plants can Shyne grow in her backyard?",
"role": "user"
},
{
"content": "I need to find the total number of plants Shyne can grow by calculating the eggplants and sunflowers separately, then adding them together.\n\nFor eggplants:\n- 14 eggplants per seed packet\n- 4 seed packets of eggplants\n- Total eggplants = 14 × 4 = 56 eggplants\n\nFor sunflowers:\n- 10 sunflowers per seed packet\n- 6 seed packets of sunflowers\n- Total sunflowers = 10 × 6 = 60 sunflowers\n\nTotal plants = 56 eggplants + 60 sunflowers = 116 plants\n\nShyne can grow 116 plants in her backyard.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "Shyne can grow 14 x 4 = 56 eggplants. She can grow 10 x 6 = 60 sunflowers. So, she can grow a total of 56 + 60 = 116 plants in her backyard.",
"incorrect_answer": "Shyne can grow 14 x 6 = 84 eggplants. She can grow 10 x 4 = 40 sunflowers. So, she can grow a total of 84 + 40 = 124 plants in her backyard.",
"messages": [
{
"content": "Shyne can grow 14 eggplants in every seed packet and 10 sunflowers in every seed packet. She bought 4 seed packets of eggplants and 6 seed packets of sunflower, how many plants can Shyne grow in her backyard?",
"role": "user"
},
{
"content": "Shyne can grow 14 x 4 = <<14*4=56>>56 eggplants.\nShe can grow 10 x 6 = <<10*6=60>>60 sunflowers.\nSo, she can grow a total of 56 + 60 = <<56+60=116>>116 plants in her backyard.\n#### 116",
"role": "assistant"
}
],
"short_incorrect_solution": "124",
"short_solution": "116"
}
|
[
{
"content": "In the Oprah Winfrey High School marching band, each trumpet and clarinet player carries 5 pounds of weight, each trombone player carries 10 pounds of weight, each tuba player carries 20 pounds of weight, and each drum player carries 15 pounds of weight. If there are 6 trumpets, 9 clarinets, 8 trombones, 3 tubas, and 2 drummers, how much weight does the total marching band carry?",
"role": "user"
},
{
"content": "I need to calculate the total weight carried by all the marching band members.\n\nLet me break this down by instrument type:\n\nTrumpets:\n- 6 trumpet players × 5 pounds each = 30 pounds\n\nClarinets:\n- 9 clarinet players × 5 pounds each = 45 pounds\n\nTrombones:\n- 8 trombone players × 10 pounds each = 80 pounds\n\nTubas:\n- 3 tuba players × 20 pounds each = 60 pounds\n\nDrummers:\n- 2 drum players × 15 pounds each = 30 pounds\n\nTotal weight:\n30 + 45 + 80 + 60 + 30 = 245 pounds\n\nThe total marching band carries 245 pounds of weight.",
"role": "assistant"
}
] | true
|
{
"correct_answer": "First find the total number of clarinet and trumpet players: 6 players + 9 players = 15 players. Then find the total weight of the trumpets and clarinets: 15 players * 5 pounds/player = 75 pounds. Then find the total weight of the trombones: 8 players * 10 pounds/player = 80 pounds. Then find the total weight of the tubas: 3 players * 20 pounds/player = 60 pounds. Then find the total weight of the drummers: 2 drummers * 15 pounds/player = 30 pounds. Then add the weight of each type of instrument to find the total weight: 75 pounds + 80 pounds + 60 pounds + 30 pounds = 245 pounds",
"incorrect_answer": "First find the total weight of the trumpets: 6 players * 5 pounds/player = 30 pounds. Then find the total weight of the clarinets: 9 players * 5 pounds/player = 45 pounds. Then find the total weight of the trombones: 8 players * 10 pounds/player = 80 pounds. Then find the total weight of the tubas: 3 players * 20 pounds/player = 60 pounds. Then find the total weight of the drummers: 2 drummers * 15 pounds/player = 30 pounds. Then add the weight of each type of instrument to find the total weight: 30 pounds + 45 pounds + 80 pounds + 60 pounds = 215 pounds",
"messages": [
{
"content": "In the Oprah Winfrey High School marching band, each trumpet and clarinet player carries 5 pounds of weight, each trombone player carries 10 pounds of weight, each tuba player carries 20 pounds of weight, and each drum player carries 15 pounds of weight. If there are 6 trumpets, 9 clarinets, 8 trombones, 3 tubas, and 2 drummers, how much weight does the total marching band carry?",
"role": "user"
},
{
"content": "First find the total number of clarinet and trumpet players: 6 players + 9 players = <<6+9=15>>15 players\nThen find the total weight of the trumpets and clarinets: 15 players * 5 pounds/player = <<15*5=75>>75 pounds\nThen find the total weight of the trombones: 8 players * 10 pounds/player = <<8*10=80>>80 pounds\nThen find the total weight of the tubas: 3 players * 20 pounds/player = <<3*20=60>>60 pounds\nThen find the total weight of the drummers: 2 drummers * 15 pounds/player = <<2*15=30>>30 pounds\nThen add the weight of each type of instrument to find the total weight: 75 pounds + 80 pounds + 60 pounds + 30 pounds = <<75+80+60+30=245>>245 pounds\n#### 245",
"role": "assistant"
}
],
"short_incorrect_solution": "215 pounds",
"short_solution": "245 pounds"
}
|
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