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[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nPeter is eating chips. Each chip is 10 calories. A bag has 24 chips and costs $2. If he wants to eat 480 calories, how much does he have to spend on chips?\n\n### Answer:\n", "role": "user" }, { "conte...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nPeter is eating chips. Each chip is 10 calories. A bag has 24 chips and costs $2. If he wants to eat 480 calories, how much does he have to spend on chips?\n\n### Answer:\n", "role": "user" }, { "conte...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nThe three-digit positive integer $N$ has a ones digit of 3. What is the probability that $N$ is divisible by X? Express your answer as a common fraction. The answer is 3. What is the value of unknown variable X?\n...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nThe three-digit positive integer $N$ has a ones digit of 3. What is the probability that $N$ is divisible by X? Express your answer as a common fraction. The answer is 3. What is the value of unknown variable X?\n...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIf Casey is considering hiring either one of two employees, where one works for $20 an hour and the other works for $22 an hour with a $6/hour subsidy from the government for hiring a disabled worker, how much mon...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIf Casey is considering hiring either one of two employees, where one works for $20 an hour and the other works for $22 an hour with a $6/hour subsidy from the government for hiring a disabled worker, how much mon...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nSara makes cakes during the five weekdays to sell on weekends. She makes 4 cakes a day and sells her cakes for $8. In 4 weeks she managed to sell all the cakes. How much money did she collect during that time?\n\n...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nSara makes cakes during the five weekdays to sell on weekends. She makes 4 cakes a day and sells her cakes for $8. In 4 weeks she managed to sell all the cakes. How much money did she collect during that time?\n\n...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nWhat is the least positive three-digit multiple of 7?\n\n### Answer:\n", "role": "user" }, { "content": "The smallest three-digit number is 100.\nWe can divide 100 by 7 and get a remainder of 2.\nTo fi...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nWhat is the least positive three-digit multiple of 7?\n\n### Answer:\n", "role": "user" }, { "content": "To find the least positive three-digit multiple of 7, we need to find the smallest number that i...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nThe three points $(3,-5)$, $(-a + 2, 3)$, and $(2a+3,2)$ lie on the same line. What is $a$?\n\n### Answer:\n", "role": "user" }, { "content": "Since the points lie on the same line, the slopes between...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nThe three points $(3,-5)$, $(-a + 2, 3)$, and $(2a+3,2)$ lie on the same line. What is $a$?\n\n### Answer:\n", "role": "user" }, { "content": "To find the value of $a$, we need to find the slope of th...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nJohn 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 ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nJohn 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 ...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIt takes Mary 30 minutes to walk uphill 1 km from her home to school, but it takes her only 10 minutes to walk from school to home along the same route. What is her average speed, in km/hr, for the round trip?\n\n...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIt takes Mary 30 minutes to walk uphill 1 km from her home to school, but it takes her only 10 minutes to walk from school to home along the same route. What is her average speed, in km/hr, for the round trip?\n\n...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nDuring her birthday, her parents have decided to give Laura and her 2 younger brothers new cellphones. However, they are confused between the innumerable service providers. Assuming no child wants a provider that ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nDuring her birthday, her parents have decided to give Laura and her 2 younger brothers new cellphones. However, they are confused between the innumerable service providers. Assuming no child wants a provider that ...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nDetermine the value of the expression (9! * 5! * 2!) / (8! * 6!).\n\n### Answer:\n", "role": "user" }, { "content": "First, we can simplify the expression by canceling out common terms in the numerator...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nDetermine the value of the expression (9! * 5! * 2!) / (8! * 6!).\n\n### Answer:\n", "role": "user" }, { "content": "To solve this problem, we will follow these steps:\n\nStep 1: Combine the factorials...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nOn his calculator, August had solved a math problem with an answer of 600. The following math problem had an answer twice as big as the answer of the first math problem, and the third math problem had an answer 40...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nOn his calculator, August had solved a math problem with an answer of 600. The following math problem had an answer twice as big as the answer of the first math problem, and the third math problem had an answer 40...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIf Fatima has a piece of cloth that is initially 100 square inches in size and she decides to cut it in half, keeping one half and donating the other half, and repeats this process two times, what is the total amo...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIf Fatima has a piece of cloth that is initially 100 square inches in size and she decides to cut it in half, keeping one half and donating the other half, and repeats this process two times, what is the total amo...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nSolve the inequality\n\\[-4x^2 + 7x + 2 < 0.\\]\n\n### Answer:\n", "role": "user" }, { "content": "First, we factor the quadratic: $-4x^2 + 7x + 2 = (x - 2)(-4x - 1)$.\nNext, we find the critical point...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nSolve the inequality\n\\[-4x^2 + 7x + 2 < 0.\\]\n\n### Answer:\n", "role": "user" }, { "content": "To solve the inequality, we first find the roots of the corresponding quadratic equation.\n\nFor that,...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nA chess team has $26$ members. However, only X members attended the last meeting: half of the girls attended but all of the boys attended. How many girls are on the chess team?\nIf we know the answer to the above ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nA chess team has $26$ members. However, only X members attended the last meeting: half of the girls attended but all of the boys attended. How many girls are on the chess team?\nIf we know the answer to the above ...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nHow many pairs $(a, b)$ of real numbers satisfy the condition that $10, a, b, ab$ form an arithmetic progression?\n\n### Answer:\n", "role": "user" }, { "content": "Since $10, a, b$ form an arithmetic ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nHow many pairs $(a, b)$ of real numbers satisfy the condition that $10, a, b, ab$ form an arithmetic progression?\n\n### Answer:\n", "role": "user" }, { "content": "To find all pairs ($a, b$) of real n...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIn 2004, there were some kids at a cookout. In 2005, half the number of kids came to the cookout as compared to 2004. In 2006, 2/3 as many kids came to the cookout as in 2005. If there were 20 kids at the cookout ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIn 2004, there were some kids at a cookout. In 2005, half the number of kids came to the cookout as compared to 2004. In 2006, 2/3 as many kids came to the cookout as in 2005. If there were 20 kids at the cookout ...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIf the bus picks up Mr. Langsley at 6:00 a.m. and takes forty minutes to reach the first station, and he arrives at work at 9:00 a.m., what is the total duration in minutes from the first station to Mr. Langsley's...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIf the bus picks up Mr. Langsley at 6:00 a.m. and takes forty minutes to reach the first station, and he arrives at work at 9:00 a.m., what is the total duration in minutes from the first station to Mr. Langsley's...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nFind the remainder when $x^4 +x + 2$ is divided by $x-3$.\n\n### Answer:\n", "role": "user" }, { "content": "Using synthetic division, we have:\n\n\\[\n\\begin{array}{c\|ccccc}\n3 & 1 & 0 & 0 & 1 & 2 \\...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nFind the remainder when $x^4 +x + 2$ is divided by $x-3$.\n\n### Answer:\n", "role": "user" }, { "content": "To find the remainder when $x^4 +x + 2$ is divided by $x-3$, we can use polynomial long divi...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nThe ratio of irises to roses in Nikki's garden is 2:5. She currently has 25 roses. She is planning to add 20 more roses and enough irises to keep the same ratio. How many irises will she have in total after this a...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nThe ratio of irises to roses in Nikki's garden is 2:5. She currently has 25 roses. She is planning to add 20 more roses and enough irises to keep the same ratio. How many irises will she have in total after this a...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIn a game played by Josef and Timothy, Josef selects an integer between 1 and 1000 (inclusive). Timothy then divides 1000 by that integer and determines whether the quotient is an integer. How many integers can Jo...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIn a game played by Josef and Timothy, Josef selects an integer between 1 and 1000 (inclusive). Timothy then divides 1000 by that integer and determines whether the quotient is an integer. How many integers can Jo...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nA bottle of wine costs $20.00 today. When new tariffs are imposed in 2 months, the price of wine will increase by 25%. How much more expensive will 5 bottles of wine be in 2 months?\n\n### Answer:\n", "role"...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nA bottle of wine costs $20.00 today. When new tariffs are imposed in 2 months, the price of wine will increase by 25%. How much more expensive will 5 bottles of wine be in 2 months?\n\n### Answer:\n", "role"...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nGiven $\\begin{vmatrix} a & b \\\\ c & d \\end{vmatrix} = X find $\\begin{vmatrix} 2a & 2b \\\\ 2c & 2d \\end{vmatrix}. 20. What is the value of unknown variable X?\n\n### Answer:\n", "role": "user" }, { ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nGiven $\\begin{vmatrix} a & b \\\\ c & d \\end{vmatrix} = X find $\\begin{vmatrix} 2a & 2b \\\\ 2c & 2d \\end{vmatrix}. 20. What is the value of unknown variable X?\n\n### Answer:\n", "role": "user" }, { ...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nA building has x floors. Each floor is 3 meters high, except for the last two floors. The last two floors are each 0.5 meters higher. The building is 61 tall.\n\n### Answer:\n", "role": "user" }, { "co...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nA building has x floors. Each floor is 3 meters high, except for the last two floors. The last two floors are each 0.5 meters higher. The building is 61 tall.\n\n### Answer:\n", "role": "user" }, { "co...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nBob drove for one and a half hours at 60/mph. He then hit construction and drove for 2 hours at 45/mph. How many miles did Bob travel in those 3 and a half hours?\n\n### Answer:\n", "role": "user" }, { ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nBob drove for one and a half hours at 60/mph. He then hit construction and drove for 2 hours at 45/mph. How many miles did Bob travel in those 3 and a half hours?\n\n### Answer:\n", "role": "user" }, { ...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nJohn reels in 3 crab baskets a week. Each basket holds 4 crabs. He collects crabs twice a week. Each crab sells for $3. How much money does he make?\n\n### Answer:\n", "role": "user" }, { "content"...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nJohn reels in 3 crab baskets a week. Each basket holds 4 crabs. He collects crabs twice a week. Each crab sells for $3. How much money does he make?\n\n### Answer:\n", "role": "user" }, { "content"...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIf Alexander was 50 inches tall on his 8th birthday and grows 1/2 a foot each year, how many inches tall will he be on his 12th birthday?\n\n### Answer:\n", "role": "user" }, { "content": "\nIf 1 foot ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIf Alexander was 50 inches tall on his 8th birthday and grows 1/2 a foot each year, how many inches tall will he be on his 12th birthday?\n\n### Answer:\n", "role": "user" }, { "content": "To solve thi...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nMurtha has decided to start a pebble collection. She collects one pebble the first day and two pebbles on the second day. On each subsequent day she collects one more pebble than the previous day. How many pebbles...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nMurtha has decided to start a pebble collection. She collects one pebble the first day and two pebbles on the second day. On each subsequent day she collects one more pebble than the previous day. How many pebbles...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nThe cost of purchasing x commodities is $827. If the purchase price of the first one exceeds the other by $127, The purchase price of the first commodity is 477.\n\n### Answer:\n", "role": "user" }, { ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nThe cost of purchasing x commodities is $827. If the purchase price of the first one exceeds the other by $127, The purchase price of the first commodity is 477.\n\n### Answer:\n", "role": "user" }, { ...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nAn insect has just told me that she has laid $154_6$ eggs. In base 10, how many eggs did she lay?\n\n### Answer:\n", "role": "user" }, { "content": "The number $154_6$ means $1\\cdot6^2+5\\cdot6^1+4\\c...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nAn insect has just told me that she has laid $154_6$ eggs. In base 10, how many eggs did she lay?\n\n### Answer:\n", "role": "user" }, { "content": "To convert a number from base 6 to base 10, we can u...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nJennifer decides to share her sweets between herself and her x friends. She has 212 green sweets, 310 blue sweets and 502 yellow sweets. How many sweets will Jennifer and her friends get each?\nIf we know the answ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nJennifer decides to share her sweets between herself and her x friends. She has 212 green sweets, 310 blue sweets and 502 yellow sweets. How many sweets will Jennifer and her friends get each?\nIf we know the answ...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nA papaya tree will grow 2 feet in the first year. In the second year, it will grow 50% more than the first year. In the third year, the tree will grow 50% more than in the second year. In the fourth year, it wi...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nA papaya tree will grow 2 feet in the first year. In the second year, it will grow 50% more than the first year. In the third year, the tree will grow 50% more than in the second year. In the fourth year, it wi...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nKim earned scores of 87, 83 and 88 on her first three mathematics examinations. If Kim receives a score of 90 on the fourth exam, then by how much will her average increase?\n\n### Answer:\n", "role": "user" ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nKim earned scores of 87, 83 and 88 on her first three mathematics examinations. If Kim receives a score of 90 on the fourth exam, then by how much will her average increase?\n\n### Answer:\n", "role": "user" ...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nWhile at the lake, Cohen saw x fish-eater birds that had migrated into the area recently walking by the lake, eating the fish they had caught. The number of birds at the lake doubled on the second day and reduced ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nWhile at the lake, Cohen saw x fish-eater birds that had migrated into the area recently walking by the lake, eating the fish they had caught. The number of birds at the lake doubled on the second day and reduced ...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIf Karen is choosing between two winter coats, one costing $300 and lasting for 15 years, and the other costing $120 and lasting for five years, how much money would she save over a 30-year period by purchasing th...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIf Karen is choosing between two winter coats, one costing $300 and lasting for 15 years, and the other costing $120 and lasting for five years, how much money would she save over a 30-year period by purchasing th...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nOn the night of the dance, 400 students show up to the party. 70% of the students who showed up were invited. If x% of those invited to the party had their invitation revoked and were not allowed into the party, h...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nOn the night of the dance, 400 students show up to the party. 70% of the students who showed up were invited. If x% of those invited to the party had their invitation revoked and were not allowed into the party, h...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nPeter needs 80 ounces of soda for his party. He sees that 8 oz cans cost $.5 each. How much does he spend on soda if he buys the exact number of cans he needs?\n\n### Answer:\n", "role": "user" }, { "c...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nPeter needs 80 ounces of soda for his party. He sees that 8 oz cans cost $.5 each. How much does he spend on soda if he buys the exact number of cans he needs?\n\n### Answer:\n", "role": "user" }, { "c...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIf Mary buys 5 apples, 3 oranges, and 2 bananas from the store where apples cost $1, oranges cost $2, and bananas cost $3, and for every 5 fruits, the store offers a $1 discount, what is the total amount that Mary...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nIf Mary buys 5 apples, 3 oranges, and 2 bananas from the store where apples cost $1, oranges cost $2, and bananas cost $3, and for every 5 fruits, the store offers a $1 discount, what is the total amount that Mary...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nWhat is the value of the ceiling function applied to -2.4?\n\n### Answer:\n", "role": "user" }, { "content": "The ceiling function of a real number $x$, denoted by $\\lceil x \\rceil$, is the smallest ...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nWhat is the value of the ceiling function applied to -2.4?\n\n### Answer:\n", "role": "user" }, { "content": "To find the value of the ceiling function applied to -2.4, we need to follow these steps:\n...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nAt Frank's Fruit Market, 3 bananas cost as much as 2 apples, and X apples cost as much as 4 oranges. Eight oranges cost as much as 18 bananas. What is the value of unknown variable X?\n\n### Answer:\n", "role"...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nAt Frank's Fruit Market, 3 bananas cost as much as 2 apples, and X apples cost as much as 4 oranges. Eight oranges cost as much as 18 bananas. What is the value of unknown variable X?\n\n### Answer:\n", "role"...
[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nThe equation of the line shown can be written as $y=mx+b$. Find $mb$.\n[asy]\nsize(100,0);\nadd(shift(-5,-5)*grid(10,10));\ndraw((-5,0)--(5,0),linewidth(2));\ndraw((0,-5)--(0,5),linewidth(2));\nlabel(\"\",(5,0),E...	[ { "content": "Below is a math problem. Provide a detailed, step-by-step solution.\n\n### Problem:\nThe equation of the line shown can be written as $y=mx+b$. Find $mb$.\n[asy]\nsize(100,0);\nadd(shift(-5,-5)*grid(10,10));\ndraw((-5,0)--(5,0),linewidth(2));\ndraw((0,-5)--(0,5),linewidth(2));\nlabel(\"\",(5,0),E...