id stringlengths 15 18 | gsm8k_index int64 0 7.47k | question stringlengths 42 985 | reasoning stringlengths 16 1.79k | solution stringlengths 51 2.44k | answer stringclasses 869
values |
|---|---|---|---|---|---|
gsm8k-train-0-0 | 0 | Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May? | We need total clips? She sold clips to 48 friends in April, then half as many clips in May. Means number of clips sold in May = half of 48 = 24. Total = 48+24=72. | **Step‑by‑step solution**
1. In April Natalia sold clips to **48** friends.
2. In May she sold **half as many** clips as in April.
\[
\text{May sales} = \frac{1}{2}\times 48 = 24
\]
3. Add the two months together:
\[
\text{Total clips} = 48 + 24 = 72
\]
**Final answer:** 72 | 72 |
gsm8k-train-0-1 | 0 | Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May? | We need total clips? She sold clips to 48 friends in April, then half as many clips in May. Probably each friend got one clip? So April 48 clips, May half as many = 24. Total 72. | **Step‑by‑step solution**
1. In April Natalia sold clips to **48** friends.
→ This means she sold **48** clips in April.
2. In May she sold “half as many clips” as she did in April.
→ Half of 48 is \( \frac{48}{2}=24 \).
→ She sold **24** clips in May.
3. To find the total number of clips sold in the ... | 72 |
gsm8k-train-0-2 | 0 | Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May? | We need total clips. She sold clips to 48 friends in April. Probably one clip each? It says sold clips to 48 friends, then half as many clips in May. So May she sold half as many clips as April: 48/2 = 24. Total = 48+24=72. | **Step‑by‑step solution**
1. In April Natalia sold clips to **48** friends.
2. In May she sold **half as many** clips as she did in April.
\[
\text{May sales} = \frac{1}{2}\times 48 = 24
\]
3. The total number of clips sold in both months is the sum of the April and May sales:
\[
\text{Total} = 48... | 72 |
gsm8k-train-0-3 | 0 | Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May? | We need total clips? She sold clips to 48 friends in April, then half as many clips in May. Assuming one clip per friend? Likely number of clips equals number of friends. So April 48 clips, May half = 24. Total = 72. | **Step‑by‑step solution**
1. In April Natalia sold clips to **48** friends, so she sold **48** clips.
2. In May she sold **half as many** clips as in April.
Half of 48 is \( \frac{48}{2}=24 \). So she sold **24** clips in May.
3. To find the total number of clips sold in both months, add the two amounts:
\(4... | 72 |
gsm8k-train-0-4 | 0 | Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May? | We need compute: 48 friends in April, sold clips to each? Probably one clip each. So 48 clips April. In May sold half as many clips: half of 48 = 24. Total = 72. | **Step‑by‑step solution**
1. In April Natalia sold clips to **48** friends, so she sold **48** clips.
2. In May she sold half as many clips as in April.
Half of 48 is \( \frac{48}{2}=24 \) clips.
3. Total clips sold in the two months = clips in April + clips in May
\( = 48 + 24 = 72 \).
**Final answer:** 72 | 72 |
gsm8k-train-1-0 | 1 | Weng earns $12 an hour for babysitting. Yesterday, she just did 50 minutes of babysitting. How much did she earn? | We calculate 12 dollars per hour, 50 minutes = 50/60 hour = 5/6 hour. Earnings = 12 * 5/6 = 10. So final answer 10. | **Step 1: Convert minutes to hours**
50 minutes ÷ 60 minutes per hour = \(\frac{50}{60} = \frac{5}{6}\) hour.
**Step 2: Calculate earnings**
Weng earns \$12 per hour.
Earnings = \$12 × \(\frac{5}{6}\) = \(\frac{12 \times 5}{6} = \frac{60}{6} = \$10\).
**Final answer:**
Final answer: 10 | 10 |
gsm8k-train-1-1 | 1 | Weng earns $12 an hour for babysitting. Yesterday, she just did 50 minutes of babysitting. How much did she earn? | We need compute 12 dollars per hour, 50 minutes = 50/60 hour = 5/6 hour. Earnings = 12 * 5/6 = 10. So final answer 10. | **Step 1: Convert the time worked to hours**
- Weng worked 50 minutes.
- There are 60 minutes in an hour, so
\[
\text{Hours worked} = \frac{50}{60} = \frac{5}{6}\text{ hour}
\]
**Step 2: Determine earnings per hour**
- Weng’s rate is \$12 per hour.
**Step 3: Multiply the hourly rate by the fraction of an hour... | 10 |
gsm8k-train-1-2 | 1 | Weng earns $12 an hour for babysitting. Yesterday, she just did 50 minutes of babysitting. How much did she earn? | We compute 12 dollars per hour, 50 minutes = 50/60 = 5/6 hour. Earnings = 12 * (5/6) = 12*5/6 = (12/6)*5 = 2*5 = 10. So $10. | **Step‑by‑step solution**
1. **Determine the fraction of an hour worked.**
\(50\) minutes \(= \dfrac{50}{60}\) hour \(= \dfrac{5}{6}\) hour.
2. **Calculate earnings per hour.**
Weng earns \(\$12\) for each full hour.
3. **Multiply the hourly rate by the fraction of an hour worked.**
\[
\text{Earnin... | 10 |
gsm8k-train-1-3 | 1 | Weng earns $12 an hour for babysitting. Yesterday, she just did 50 minutes of babysitting. How much did she earn? | We need compute 12 per hour, 50 minutes = 50/60 hour = 5/6 hour. Earnings = 12 * (5/6) = 12 * 0.83333 = 10. So $10. | **Step 1: Convert minutes to hours**
50 minutes ÷ 60 minutes per hour = \( \frac{50}{60} = \frac{5}{6} \) hour.
**Step 2: Calculate earnings**
Hourly rate = $12.
Earnings = $12 × \( \frac{5}{6} \) = \( \frac{12 \times 5}{6} = \frac{60}{6} = 10 \).
**Final answer:**
Final answer: 10 | 10 |
gsm8k-train-1-4 | 1 | Weng earns $12 an hour for babysitting. Yesterday, she just did 50 minutes of babysitting. How much did she earn? | We compute hourly rate $12 per hour. 50 minutes = 50/60 = 5/6 hour. Earnings = 12 * 5/6 = 10. So final answer 10 dollars. | **Step 1: Convert the time worked to hours**
- 50 minutes ÷ 60 minutes per hour = \( \frac{50}{60} = \frac{5}{6} \) hour.
**Step 2: Calculate earnings**
- Hourly wage = $12 per hour.
- Earnings = hourly wage × hours worked
\( = 12 \times \frac{5}{6} = \frac{12 \times 5}{6} = \frac{60}{6} = 10 \).
**Step 3: ... | 10 |
gsm8k-train-2-0 | 2 | Betty is saving money for a new wallet which costs $100. Betty has only half of the money she needs. Her parents decided to give her $15 for that purpose, and her grandparents twice as much as her parents. How much more money does Betty need to buy the wallet? | We compute: wallet 100. Betty has half = 50. Parents give 15. Grandparents give twice as much as parents = 30. Total after gifts = 50+15+30=95. Need 5 more. | **Step‑by‑step solution**
1. **Cost of the wallet:** \$100.
2. **Betty’s current savings:** She has half of the needed amount →
\( \frac{1}{2} \times 100 = \$50\).
3. **Money from parents:** \$15.
4. **Money from grandparents:** They give twice what the parents give →
\(2 \times 15 = \$30\).
5. **Total ... | 5 |
gsm8k-train-2-1 | 2 | Betty is saving money for a new wallet which costs $100. Betty has only half of the money she needs. Her parents decided to give her $15 for that purpose, and her grandparents twice as much as her parents. How much more money does Betty need to buy the wallet? | We compute: wallet 100. Betty has half = 50. Parents give 15. Grandparents give twice as much as parents = 30. Total after gifts = 50+15+30 = 95. Need 5 more. | **Step‑by‑step solution**
1. **Cost of the wallet:** \$100.
2. **Betty’s current savings:** She has half of the needed amount, so
\[
\frac{1}{2}\times 100 = \$50.
\]
3. **Money from her parents:** \$15.
4. **Money from her grandparents:** They give twice what the parents give, so
\[
2 \times 15 ... | 5 |
gsm8k-train-2-2 | 2 | Betty is saving money for a new wallet which costs $100. Betty has only half of the money she needs. Her parents decided to give her $15 for that purpose, and her grandparents twice as much as her parents. How much more money does Betty need to buy the wallet? | We compute: wallet 100. Betty has half = 50. Parents give 15, grandparents give twice as much = 30. So total after gifts = 50+15+30 = 95. Need 5 more. | **Step‑by‑step solution**
1. **Cost of the wallet:** \$100.
2. **Betty’s current savings:** she has half of the needed amount →
\[
\frac{1}{2}\times 100 = \$50.
\]
3. **Money from parents:** \$15.
4. **Money from grandparents:** twice the parents’ contribution →
\[
2 \times 15 = \$30.
\]
5. ... | 5 |
gsm8k-train-2-3 | 2 | Betty is saving money for a new wallet which costs $100. Betty has only half of the money she needs. Her parents decided to give her $15 for that purpose, and her grandparents twice as much as her parents. How much more money does Betty need to buy the wallet? | We compute: wallet 100, Betty has half = 50. Parents give 15, grandparents give twice as much = 30. Total now = 50+15+30=95. Needs 5 more. | **Step‑by‑step solution**
1. **Cost of the wallet:** \$100.
2. **Betty’s current savings:** she has half of what she needs → \( \frac{1}{2}\times100 = \$50\).
3. **Parents’ contribution:** \$15.
4. **Grandparents’ contribution:** twice the parents’ amount → \(2 \times 15 = \$30\).
5. **Total money Betty will h... | 5 |
gsm8k-train-2-4 | 2 | Betty is saving money for a new wallet which costs $100. Betty has only half of the money she needs. Her parents decided to give her $15 for that purpose, and her grandparents twice as much as her parents. How much more money does Betty need to buy the wallet? | We compute: wallet 100, Betty has half = 50. Parents give 15, grandparents give twice as much = 30. Total after gifts: 50+15+30=95. Needs 5 more. | **Step‑by‑step solution**
1. **Cost of the wallet:** \$100.
2. **Betty’s current savings:** She has half of the needed amount →
\[
\frac{100}{2}= \$50
\]
3. **Money from her parents:** \$15.
4. **Money from her grandparents:** twice what the parents give →
\[
2 \times 15 = \$30
\]
5. **Total ... | 5 |
gsm8k-train-3-0 | 3 | Julie is reading a 120-page book. Yesterday, she was able to read 12 pages and today, she read twice as many pages as yesterday. If she wants to read half of the remaining pages tomorrow, how many pages should she read? | We compute: total 120. Yesterday 12. Today twice as many = 24. So read so far = 36. Remaining = 84. She wants to read half of remaining tomorrow: half of 84 = 42. So answer 42. | **Step 1: Determine how many pages Julie has already read.**
- Yesterday: 12 pages
- Today: twice as many as yesterday → \(2 \times 12 = 24\) pages
Total read so far = \(12 + 24 = 36\) pages.
**Step 2: Find the number of pages left to read.**
- The book has 120 pages.
- Remaining pages = \(120 - 36 = 84\) p... | 42 |
gsm8k-train-3-1 | 3 | Julie is reading a 120-page book. Yesterday, she was able to read 12 pages and today, she read twice as many pages as yesterday. If she wants to read half of the remaining pages tomorrow, how many pages should she read? | We compute: total 120. Yesterday 12. Today twice as many = 24. So read so far 12+24=36. Remaining = 84. She wants to read half of remaining tomorrow: half of 84 = 42. So answer 42. | **Step 1: Determine how many pages Julie read yesterday.**
She read \(12\) pages.
**Step 2: Determine how many pages she read today.**
Today she read twice as many pages as yesterday:
\(2 \times 12 = 24\) pages.
**Step 3: Find the total number of pages read so far.**
\(12 + 24 = 36\) pages.
**Step 4: Calcula... | 42 |
gsm8k-train-3-2 | 3 | Julie is reading a 120-page book. Yesterday, she was able to read 12 pages and today, she read twice as many pages as yesterday. If she wants to read half of the remaining pages tomorrow, how many pages should she read? | We compute: total 120. Yesterday 12. Today twice as many = 24. So read so far = 36. Remaining = 84. She wants to read half of remaining tomorrow = 42. Answer 42. | **Step‑by‑step solution**
1. Total pages in the book: 120.
2. Yesterday she read 12 pages.
3. Today she read twice as many as yesterday: \(2 \times 12 = 24\) pages.
4. Pages read so far: \(12 + 24 = 36\) pages.
5. Remaining pages: \(120 - 36 = 84\) pages.
6. She wants to read half of the remaining pages tomo... | 42 |
gsm8k-train-3-3 | 3 | Julie is reading a 120-page book. Yesterday, she was able to read 12 pages and today, she read twice as many pages as yesterday. If she wants to read half of the remaining pages tomorrow, how many pages should she read? | We compute: total 120. Yesterday 12. Today twice as many = 24. So read so far 12+24=36. Remaining = 120-36=84. She wants to read half of remaining tomorrow: half of 84 = 42. Answer 42. | **Step 1: Determine pages read so far**
- Yesterday: 12 pages
- Today: twice as many as yesterday → \(2 \times 12 = 24\) pages
Total read after two days:
\(12 + 24 = 36\) pages
**Step 2: Find remaining pages**
Total pages in the book = 120
Remaining pages = \(120 - 36 = 84\) pages
**Step 3: Compute h... | 42 |
gsm8k-train-3-4 | 3 | Julie is reading a 120-page book. Yesterday, she was able to read 12 pages and today, she read twice as many pages as yesterday. If she wants to read half of the remaining pages tomorrow, how many pages should she read? | We calculate: total 120. Yesterday 12. Today read twice as many as yesterday = 24. So read so far 12+24=36. Remaining = 120-36=84. She wants to read half of the remaining pages tomorrow: half of 84 = 42. So answer 42. | **Step‑by‑step solution**
1. **Pages read yesterday:** 12 pages.
2. **Pages read today:** twice as many as yesterday → \(2 \times 12 = 24\) pages.
3. **Total pages read so far:** \(12 + 24 = 36\) pages.
4. **Pages left to read:** \(120 - 36 = 84\) pages.
5. **Pages to read tomorrow:** half of the remaining pag... | 42 |
gsm8k-train-4-0 | 4 | James writes a 3-page letter to 2 different friends twice a week. How many pages does he write a year? | Compute: 3 pages per letter, 2 friends = 2 letters per session? Actually writes a 3-page letter to 2 different friends twice a week. Means each week, he writes two letters (one to each friend) and does this twice a week? Could be ambiguous: He writes a 3-page letter to 2 different friends twice a week. Likely means eac... | **Step‑by‑step calculation**
1. Each letter is **3 pages** long.
2. He writes a letter to **2 different friends** each time, so that is **2 letters** per writing session.
3. He does this **twice a week**, so the number of letters per week is
\[
2 \text{ letters per session} \times 2 \text{ sessions per wee... | 624 |
gsm8k-train-4-1 | 4 | James writes a 3-page letter to 2 different friends twice a week. How many pages does he write a year? | We compute: 3 pages per letter, 2 friends = 2 letters per session, twice a week = 2 times per week. So pages per week = 3*2*2 =12 pages. Weeks per year ~52. So yearly pages =12*52=624. Possibly consider 52 weeks exactly. So final answer 624. | **Step‑by‑step calculation**
1. **Pages per letter:** 3 pages.
2. **Letters per writing session:** He writes a letter to each of 2 friends → \(2\) letters.
3. **Pages per session:** \(3 \text{ pages} \times 2 = 6\) pages.
4. **Sessions per week:** He writes twice a week → \(2\) sessions.
5. **Pages per week:**... | 624 |
gsm8k-train-4-2 | 4 | James writes a 3-page letter to 2 different friends twice a week. How many pages does he write a year? | Compute: 3 pages per letter, 2 friends = 2 letters per occasion, twice a week = 2 times per week. So per week pages = 3*2*2 =12 pages. Weeks per year ~52. So 12*52=624 pages. Might consider 52 weeks exactly. So final answer 624. | **Step‑by‑step solution**
1. **Pages per letter:** 3 pages.
2. **Letters per writing session:** He writes a letter to each of 2 friends → \(2\) letters.
3. **Pages per session:** \(3 \text{ pages/letter} \times 2 \text{ letters}=6\) pages.
4. **Sessions per week:** He writes twice a week → \(2\) sessions.
5. *... | 624 |
gsm8k-train-4-3 | 4 | James writes a 3-page letter to 2 different friends twice a week. How many pages does he write a year? | We compute: 3 pages per letter, 2 friends = 2 letters per session, twice a week = 2 times per week. So per week pages = 3 * 2 * 2 = 12 pages. Weeks per year ~ 52. So yearly = 12 * 52 = 624 pages. Might consider 52 weeks exactly. So final answer 624. | **Step‑by‑step solution**
1. **Pages per letter:** 3 pages
2. **Letters per writing session:** He writes to 2 different friends → \(2\) letters
3. **Pages per writing session:** \(3 \text{ pages/letter} \times 2 \text{ letters}=6\) pages
4. **Sessions per week:** He writes twice a week → \(2\) sessions
5. **Pa... | 624 |
gsm8k-train-4-4 | 4 | James writes a 3-page letter to 2 different friends twice a week. How many pages does he write a year? | We calculate: 3 pages per letter, 2 friends = 2 letters per session, twice a week => 2 letters * 2 times = 4 letters per week. Each letter 3 pages, so 4*3=12 pages per week. Weeks per year ~52. So 12*52=624 pages. Might consider 52 weeks exactly. So final answer 624. | **Step‑by‑step calculation**
1. **Pages per letter:** 3 pages
2. **Letters per week:** He writes a letter to each of 2 friends **twice** a week.
\(2 \text{ friends} \times 2 \text{ times/week} = 4 \text{ letters/week}\)
3. **Pages per week:**
\(4 \text{ letters/week} \times 3 \text{ pages/letter} = 12 \te... | 624 |
gsm8k-train-5-0 | 5 | Mark has a garden with flowers. He planted plants of three different colors in it. Ten of them are yellow, and there are 80% more of those in purple. There are only 25% as many green flowers as there are yellow and purple flowers. How many flowers does Mark have in his garden? | We need interpret: 10 yellow. Purple are 80% more than yellow, meaning purple = yellow + 0.8*yellow = 1.8*yellow = 18? 10*1.8 = 18. So purple = 18.
Green are 25% as many as there are yellow and purple flowers combined. So green = 0.25*(yellow+purple) = 0.25*(10+18)=0.25*28=7.
Total = 10+18+7 = 35.
Check integer okay... | Let
- \(Y\) = number of yellow flowers
- \(P\) = number of purple flowers
- \(G\) = number of green flowers
**Step 1: Yellow flowers**
\(Y = 10\).
**Step 2: Purple flowers**
“80 % more of those in purple” means the purple count is 80 % greater than the yellow count:
\[
P = Y + 0.80Y = 1.80Y = 1.8 \times... | 35 |
gsm8k-train-5-1 | 5 | Mark has a garden with flowers. He planted plants of three different colors in it. Ten of them are yellow, and there are 80% more of those in purple. There are only 25% as many green flowers as there are yellow and purple flowers. How many flowers does Mark have in his garden? | We need variables: Y=10 yellow. Purple = 80% more than yellow => 80% more means 1.8 times? 80% more than Y = Y + 0.8Y = 1.8Y = 18? Y=10 so P=18.
Green = 25% as many as there are yellow and purple flowers combined. So G = 0.25*(Y+P) = 0.25*(10+18)=0.25*28=7.
Total = Y+P+G =10+18+7=35.
Check: green 7 is 25% of 28, cor... | Let
- \(Y\) = number of yellow flowers = 10
- \(P\) = number of purple flowers
- \(G\) = number of green flowers
**Step 1: Find the purple flowers**
“80 % more of those in purple” means the purple count is 80 % greater than the yellow count:
\[
P = Y + 0.80Y = 1.80Y = 1.8 \times 10 = 18.
\]
**Step 2: Find... | 35 |
gsm8k-train-5-2 | 5 | Mark has a garden with flowers. He planted plants of three different colors in it. Ten of them are yellow, and there are 80% more of those in purple. There are only 25% as many green flowers as there are yellow and purple flowers. How many flowers does Mark have in his garden? | We need interpret: 10 yellow. Purple are 80% more than yellow => purple = yellow + 0.8*yellow = 1.8*yellow = 18? 10*1.8=18. So purple = 18. Green are 25% as many as there are yellow and purple combined. So green = 0.25*(yellow+purple) = 0.25*(10+18)=0.25*28=7. So total = 10+18+7 = 35. | **Step 1: Identify the number of yellow flowers**
Mark planted 10 yellow flowers.
**Step 2: Find the number of purple flowers**
The problem states there are 80 % more purple flowers than yellow ones.
\( \text{Purple} = \text{Yellow} + 0.80 \times \text{Yellow} = 1.80 \times \text{Yellow} \)
\( \text{Purple} = ... | 35 |
gsm8k-train-5-3 | 5 | Mark has a garden with flowers. He planted plants of three different colors in it. Ten of them are yellow, and there are 80% more of those in purple. There are only 25% as many green flowers as there are yellow and purple flowers. How many flowers does Mark have in his garden? | We set yellow =10. Purple is 80% more than yellow => purple = yellow * (1+0.8)=10*1.8=18. So purple =18. Total yellow+purple =28. Green is 25% as many as there are yellow and purple flowers => green = 0.25 * 28 =7. So total flowers =10+18+7=35. | **Step‑by‑step solution**
1. Let the number of yellow flowers be \(Y = 10\).
2. Purple flowers are 80 % more than the yellow ones:
\[
P = Y + 0.80Y = 1.80Y = 1.8 \times 10 = 18.
\]
3. The combined number of yellow and purple flowers is
\[
Y + P = 10 + 18 = 28.
\]
4. Green flowers are 25 % of t... | 35 |
gsm8k-train-5-4 | 5 | Mark has a garden with flowers. He planted plants of three different colors in it. Ten of them are yellow, and there are 80% more of those in purple. There are only 25% as many green flowers as there are yellow and purple flowers. How many flowers does Mark have in his garden? | We need interpret: 10 are yellow. There are 80% more of those in purple. Means purple = yellow + 80% of yellow = yellow * (1+0.8)=1.8*yellow = 1.8*10 = 18. So purple = 18.
Green flowers are only 25% as many as there are yellow and purple flowers combined. So green = 0.25*(yellow+purple) = 0.25*(10+18)=0.25*28=7.
Tota... | Step‑by‑step:
1. Yellow flowers = 10.
2. Purple flowers are 80 % more than the yellow ones:
\( \text{purple} = 10 + 0.80 \times 10 = 1.8 \times 10 = 18\).
3. The number of green flowers is 25 % of the total of yellow + purple flowers:
\( \text{green} = 0.25 \times (10 + 18) = 0.25 \times 28 = 7\).
4. T... | 35 |
gsm8k-train-6-0 | 6 | Albert is wondering how much pizza he can eat in one day. He buys 2 large pizzas and 2 small pizzas. A large pizza has 16 slices and a small pizza has 8 slices. If he eats it all, how many pieces does he eat that day? | Simple multiplication. 2 large *16 =32, 2 small *8=16, total 48. | **Step‑by‑step solution**
1. **Large pizzas**
- Each large pizza has 16 slices.
- Albert buys 2 large pizzas.
- Total slices from large pizzas = \(2 \times 16 = 32\).
2. **Small pizzas**
- Each small pizza has 8 slices.
- Albert buys 2 small pizzas.
- Total slices from small pizzas = \(2... | 48 |
gsm8k-train-6-1 | 6 | Albert is wondering how much pizza he can eat in one day. He buys 2 large pizzas and 2 small pizzas. A large pizza has 16 slices and a small pizza has 8 slices. If he eats it all, how many pieces does he eat that day? | Compute: 2 large *16 =32, 2 small *8 =16, total 48. | **Step‑by‑step solution**
1. Determine the number of slices in the large pizzas:
\(2 \text{ large pizzas} \times 16 \text{ slices per large pizza}=32 \text{ slices}\).
2. Determine the number of slices in the small pizzas:
\(2 \text{ small pizzas} \times 8 \text{ slices per small pizza}=16 \text{ slices}\).... | 48 |
gsm8k-train-6-2 | 6 | Albert is wondering how much pizza he can eat in one day. He buys 2 large pizzas and 2 small pizzas. A large pizza has 16 slices and a small pizza has 8 slices. If he eats it all, how many pieces does he eat that day? | Just compute. 2 large *16=32, 2 small*8=16, total 48. | **Step‑by‑step solution**
1. Determine the number of slices in the large pizzas:
\(2 \text{ large pizzas} \times 16 \text{ slices per large pizza}=32 \text{ slices}\).
2. Determine the number of slices in the small pizzas:
\(2 \text{ small pizzas} \times 8 \text{ slices per small pizza}=16 \text{ slices}\).... | 48 |
gsm8k-train-6-3 | 6 | Albert is wondering how much pizza he can eat in one day. He buys 2 large pizzas and 2 small pizzas. A large pizza has 16 slices and a small pizza has 8 slices. If he eats it all, how many pieces does he eat that day? | Simple arithmetic. 2 large *16 =32, 2 small *8=16, total 48. | **Step‑by‑step solution**
1. **Large pizzas**
- Each large pizza has 16 slices.
- Albert buys 2 large pizzas.
- Total slices from large pizzas = \(2 \times 16 = 32\).
2. **Small pizzas**
- Each small pizza has 8 slices.
- Albert buys 2 small pizzas.
- Total slices from small pizzas = \(2... | 48 |
gsm8k-train-6-4 | 6 | Albert is wondering how much pizza he can eat in one day. He buys 2 large pizzas and 2 small pizzas. A large pizza has 16 slices and a small pizza has 8 slices. If he eats it all, how many pieces does he eat that day? | Simple multiplication. | **Step‑by‑step solution**
1. **Large pizzas**
- Number of large pizzas: 2
- Slices per large pizza: 16
- Total slices from large pizzas = \(2 \times 16 = 32\).
2. **Small pizzas**
- Number of small pizzas: 2
- Slices per small pizza: 8
- Total slices from small pizzas = \(2 \times 8 = 16... | 48 |
gsm8k-train-7-0 | 7 | Ken created a care package to send to his brother, who was away at boarding school. Ken placed a box on a scale, and then he poured into the box enough jelly beans to bring the weight to 2 pounds. Then, he added enough brownies to cause the weight to triple. Next, he added another 2 pounds of jelly beans. And final... | We track weight. Start with box weight unknown? He placed a box on a scale, then poured jelly beans to bring weight to 2 pounds. So after first step weight = 2 lbs (box+beans). Let W0 be box weight initially? Not needed. So current weight =2.
Then added brownies to cause weight to triple. So weight becomes 3*2 =6.
Ne... | Step 1: After adding jelly beans, the total weight is **2 lb**.
Step 2: Adding brownies triples the weight → \(3 \times 2 = 6\) lb.
Step 3: Adding another 2 lb of jelly beans → \(6 + 2 = 8\) lb.
Step 4: Adding gummy worms doubles the weight → \(2 \times 8 = 16\) lb.
Final answer: 16. | 16 |
gsm8k-train-7-1 | 7 | Ken created a care package to send to his brother, who was away at boarding school. Ken placed a box on a scale, and then he poured into the box enough jelly beans to bring the weight to 2 pounds. Then, he added enough brownies to cause the weight to triple. Next, he added another 2 pounds of jelly beans. And final... | We track. Let initial box weight = B. First add jelly beans to bring weight to 2 lbs: so after first step weight = 2. So B + J1 = 2 => B = 2 - J1 but not needed.
Second add brownies to triple weight: weight becomes 3*2 = 6.
Third add another 2 pounds of jelly beans: weight = 6 + 2 = 8.
Finally add gummy worms to dou... | Step 1: After adding jelly beans, the total weight is 2 lb.
Step 2: Adding brownies triples the weight → \(3 \times 2 = 6\) lb.
Step 3: Adding another 2 lb of jelly beans gives \(6 + 2 = 8\) lb.
Step 4: Adding gummy worms doubles the weight → \(2 \times 8 = 16\) lb.
Final answer: 16 | 16 |
gsm8k-train-7-2 | 7 | Ken created a care package to send to his brother, who was away at boarding school. Ken placed a box on a scale, and then he poured into the box enough jelly beans to bring the weight to 2 pounds. Then, he added enough brownies to cause the weight to triple. Next, he added another 2 pounds of jelly beans. And final... | We track weight. Start with empty box? He placed a box on a scale (weight of box unknown). Let initial weight = B (box). Then he poured jelly beans to bring weight to 2 pounds. So after adding jelly beans, total = 2. So B + J1 = 2 => J1 = 2 - B.
Then added brownies to cause weight to triple. So new weight = 3 * curren... | Step‑by‑step:
1. Let the weight of the empty box be \(B\) pounds.
After adding enough jelly beans the total weight is 2 lb:
\(B + J_1 = 2\).
2. Adding brownies triples the weight, so the new total is \(3 \times 2 = 6\) lb.
Brownies added: \(6 - 2 = 4\) lb.
3. Adding another 2 lb of jelly beans gives: ... | 16 |
gsm8k-train-7-3 | 7 | Ken created a care package to send to his brother, who was away at boarding school. Ken placed a box on a scale, and then he poured into the box enough jelly beans to bring the weight to 2 pounds. Then, he added enough brownies to cause the weight to triple. Next, he added another 2 pounds of jelly beans. And final... | We track weight.
Start: box weight? unknown, but we can treat as B. He placed box on scale (weight B). Then poured jelly beans to bring weight to 2 pounds. So after first addition weight = 2. So B + jelly beans = 2 => after step1 weight =2.
Step2: added brownies to cause weight to triple. So weight becomes 3*2 =6.
S... | Step 1: After putting the empty box on the scale, Ken adds jelly beans until the total weight is **2 lb**.
Step 2: He then adds brownies that make the weight triple:
\(2 \text{lb} \times 3 = 6 \text{lb}\).
Step 3: He adds another 2 lb of jelly beans:
\(6 \text{lb} + 2 \text{lb} = 8 \text{lb}\).
Step 4: Finally, ... | 16 |
gsm8k-train-7-4 | 7 | Ken created a care package to send to his brother, who was away at boarding school. Ken placed a box on a scale, and then he poured into the box enough jelly beans to bring the weight to 2 pounds. Then, he added enough brownies to cause the weight to triple. Next, he added another 2 pounds of jelly beans. And final... | We track. Start with empty box weight? Box weight unknown, but we consider weight after each step. Let initial box weight = B.
Step1: add jelly beans to bring weight to 2 lbs. So after step1 weight = 2.
Step2: add brownies to cause weight to triple. So weight becomes 3*2 = 6.
Step3: add another 2 lbs of jelly beans.... | Step 1: After adding jelly beans, the total weight is **2 lb**.
Step 2: Adding brownies triples the weight: \(3 \times 2 = 6\) lb.
Step 3: Adding another 2 lb of jelly beans gives \(6 + 2 = 8\) lb.
Step 4: Adding gummy worms doubles the weight: \(2 \times 8 = 16\) lb.
Final answer: 16 | 16 |
gsm8k-train-8-0 | 8 | Alexis is applying for a new job and bought a new set of business clothes to wear to the interview. She went to a department store with a budget of $200 and spent $30 on a button-up shirt, $46 on suit pants, $38 on a suit coat, $11 on socks, and $18 on a belt. She also purchased a pair of shoes, but lost the receipt fo... | We sum known expenses: 30+46+38+11+18 = 143. Budget 200, left 16, so spent total = 200-16 = 184. Shoes cost = total spent - known expenses = 184-143 = 41. | **Step‑by‑step solution**
1. **Total budget:** \$200
2. **Money left after shopping:** \$16
Therefore the total amount Alexis actually spent is
\[
200 - 16 = \$184.
\]
3. **Add up the known purchases:**
\[
\begin{aligned}
\text{Shirt} &= \$30 \\
\text{Suit pants} &= \$46 \\
\text... | 41 |
gsm8k-train-8-1 | 8 | Alexis is applying for a new job and bought a new set of business clothes to wear to the interview. She went to a department store with a budget of $200 and spent $30 on a button-up shirt, $46 on suit pants, $38 on a suit coat, $11 on socks, and $18 on a belt. She also purchased a pair of shoes, but lost the receipt fo... | We sum known expenses: 30+46+38+11+18 = 143. She had $200 budget, left $16, so spent total = 200-16 = 184. Shoes cost = total spent - known expenses = 184-143 = 41. | First, add up the amounts Alexis definitely spent:
- Shirt: \$30
- Pants: \$46
- Coat: \$38
- Socks: \$11
- Belt: \$18
\(30 + 46 + 38 + 11 + 18 = 143\)
She started with a budget of \$200 and has \$16 left, so the total amount she actually spent is:
\(200 - 16 = 184\)
The cost of the shoes is the differen... | 41 |
gsm8k-train-8-2 | 8 | Alexis is applying for a new job and bought a new set of business clothes to wear to the interview. She went to a department store with a budget of $200 and spent $30 on a button-up shirt, $46 on suit pants, $38 on a suit coat, $11 on socks, and $18 on a belt. She also purchased a pair of shoes, but lost the receipt fo... | We sum known expenses: 30+46+38+11+18 = 143. Budget 200, left 16, so spent total = 200-16 = 184. Shoes cost = 184 - 143 = 41. | First, add up the amounts Alexis knows she spent:
- Shirt: $30
- Suit pants: $46
- Suit coat: $38
- Socks: $11
- Belt: $18
\(30 + 46 + 38 + 11 + 18 = 143\) dollars.
She started with a budget of $200 and has $16 left, so the total amount she actually spent is:
\(200 - 16 = 184\) dollars.
The amount spent ... | 41 |
gsm8k-train-8-3 | 8 | Alexis is applying for a new job and bought a new set of business clothes to wear to the interview. She went to a department store with a budget of $200 and spent $30 on a button-up shirt, $46 on suit pants, $38 on a suit coat, $11 on socks, and $18 on a belt. She also purchased a pair of shoes, but lost the receipt fo... | We sum known expenses: 30+46+38+11+18 = 143. Budget 200, left 16, so spent total = 200-16 = 184. Shoes cost = 184 - 143 = 41. | First, add up the amounts Alexis definitely spent:
- Shirt: $30
- Suit pants: $46
- Suit coat: $38
- Socks: $11
- Belt: $18
Total known spending = $30 + $46 + $38 + $11 + $18 = **$143**.
Alexis had a total budget of $200 and she has $16 left.
Therefore, the amount she actually spent (including the shoes)... | 41 |
gsm8k-train-8-4 | 8 | Alexis is applying for a new job and bought a new set of business clothes to wear to the interview. She went to a department store with a budget of $200 and spent $30 on a button-up shirt, $46 on suit pants, $38 on a suit coat, $11 on socks, and $18 on a belt. She also purchased a pair of shoes, but lost the receipt fo... | We sum known purchases: 30+46+38+11+18 = 143. She had budget 200, left 16, so spent total = 200-16 = 184. Shoes cost = 184 - 143 = 41. | First, add up the amounts Alexis definitely spent:
- Shirt: $30
- Pants: $46
- Coat: $38
- Socks: $11
- Belt: $18
Total known spending = 30 + 46 + 38 + 11 + 18 = **$143**.
Alexis started with a budget of $200 and has $16 left, so the total amount she actually spent is:
$200 − $16 = **$184**.
The amount s... | 41 |
gsm8k-train-9-0 | 9 | Tina makes $18.00 an hour. If she works more than 8 hours per shift, she is eligible for overtime, which is paid by your hourly wage + 1/2 your hourly wage. If she works 10 hours every day for 5 days, how much money does she make? | We calculate: regular 8 hrs at $18 = $144 per day. Overtime 2 hrs at $18*1.5 = $27 per hr, so 2*27=54. Total per day = 144+54=198. For 5 days: 198*5=990. | **Step‑by‑step solution**
1. **Regular pay rate:** $18.00 per hour.
2. **Overtime rate:** regular rate + ½ regular rate = $18.00 + $9.00 = **$27.00 per hour**.
3. **Hours worked each day:** 10 hours.
- Regular hours (first 8 hours): 8 h × $18.00 = **$144.00**
- Overtime hours (the remaining 2 hours): 2 h ... | 990 |
gsm8k-train-9-1 | 9 | Tina makes $18.00 an hour. If she works more than 8 hours per shift, she is eligible for overtime, which is paid by your hourly wage + 1/2 your hourly wage. If she works 10 hours every day for 5 days, how much money does she make? | We compute: regular 8h at $18 = $144 per day. Overtime 2h at $18 + $9 = $27 per hour, so 2*27=54. Daily total = 144+54=198. For 5 days: 198*5 = 990. | **Step‑by‑step calculation**
1. **Regular pay rate:** \$18.00 per hour.
2. **Overtime rate:** regular rate + ½ regular rate = \$18.00 + \$9.00 = **\$27.00 per hour**.
3. **Hours worked each day:** 10 hours.
- Regular hours (first 8 hours): 8 h × \$18.00 = **\$144.00**
- Overtime hours (the extra 2 hours):... | 990 |
gsm8k-train-9-2 | 9 | Tina makes $18.00 an hour. If she works more than 8 hours per shift, she is eligible for overtime, which is paid by your hourly wage + 1/2 your hourly wage. If she works 10 hours every day for 5 days, how much money does she make? | We calculate regular 8 hrs at $18 = $144 per day. Overtime 2 hrs at $27 (1.5*18) = $54. Daily total $198. For 5 days: $198*5 = $990. | **Step‑by‑step calculation**
1. **Regular pay rate:** \$18.00 per hour.
2. **Overtime rate:** regular rate + ½ of regular rate = \$18.00 + \$9.00 = **\$27.00 per hour**.
3. **Hours worked each day:** 10 hours.
- Regular hours (first 8 hours): 8 h × \$18.00 = **\$144.00**.
- Overtime hours (the remaining 2... | 990 |
gsm8k-train-9-3 | 9 | Tina makes $18.00 an hour. If she works more than 8 hours per shift, she is eligible for overtime, which is paid by your hourly wage + 1/2 your hourly wage. If she works 10 hours every day for 5 days, how much money does she make? | We calculate: regular 8h at $18 = $144 per day. Overtime 2h at $18 + $9 = $27 per hour, so 2*27=54. Daily total = 144+54=198. For 5 days: 198*5 = 990. | **Step‑by‑step calculation**
1. **Regular pay rate:** \$18.00 per hour.
2. **Overtime rate:** regular rate + ½ regular rate = \$18 + \$9 = **\$27 per hour**.
3. **Hours worked each day:** 10 hours
- Regular hours (first 8 hours): 8 h
- Overtime hours (beyond 8): 10 h − 8 h = **2 h**
4. **Daily earnings**... | 990 |
gsm8k-train-9-4 | 9 | Tina makes $18.00 an hour. If she works more than 8 hours per shift, she is eligible for overtime, which is paid by your hourly wage + 1/2 your hourly wage. If she works 10 hours every day for 5 days, how much money does she make? | We compute regular 8 hrs at $18 = $144 per day. Overtime 2 hrs at $18 + 9 = $27 per hour. So overtime pay per day = 2*27 = $54. Total per day = 144+54 = 198. For 5 days: 198*5 = 990. So final answer 990. | **Step‑by‑step calculation**
1. **Regular hourly wage:** \$18.00 per hour.
2. **Overtime rate:** regular wage + ½ regular wage
\[
18 + \frac{1}{2}\times 18 = 18 + 9 = \$27\text{/hour}
\]
3. **Hours worked each day:** 10 hours
- First 8 hours are paid at the regular rate.
- The remaining \(10 - ... | 990 |
gsm8k-train-10-0 | 10 | A deep-sea monster rises from the waters once every hundred years to feast on a ship and sate its hunger. Over three hundred years, it has consumed 847 people. Ships have been built larger over time, so each new ship has twice as many people as the last ship. How many people were on the ship the monster ate in the firs... | We have geometric series. Total over 3 periods = 847. Let first ship have x people. Next ship double: 2x, then 4x. Sum = x+2x+4x =7x =847 => x = 121. So first hundred years ship had 121 people. Check integer. 7*121=847 correct. | Let the number of people on the first ship be \(x\).
Since each later ship has twice as many people as the previous one, the numbers of people on the three ships (one every hundred years) are:
- 1st ship: \(x\)
- 2nd ship: \(2x\)
- 3rd ship: \(4x\)
The monster ate a total of 847 people over the three hundred years, ... | 121 |
gsm8k-train-10-1 | 10 | A deep-sea monster rises from the waters once every hundred years to feast on a ship and sate its hunger. Over three hundred years, it has consumed 847 people. Ships have been built larger over time, so each new ship has twice as many people as the last ship. How many people were on the ship the monster ate in the firs... | We have geometric series. Let first ship have x people. Next each 100 years double: x, 2x,4x,... Over 300 years there are 3 ships (since every 100 years). Total consumed = x+2x+4x =7x =847. So x =847/7 =121. So answer 121. | **Step‑by‑step reasoning**
1. Let the number of people on the first ship be \(x\).
2. Each subsequent ship has twice as many people as the previous one, so the numbers of people on the three ships are
\(x,\;2x,\;4x\).
3. Over three hundred years the monster ate all three ships, so the total number of people consu... | 121 |
gsm8k-train-10-2 | 10 | A deep-sea monster rises from the waters once every hundred years to feast on a ship and sate its hunger. Over three hundred years, it has consumed 847 people. Ships have been built larger over time, so each new ship has twice as many people as the last ship. How many people were on the ship the monster ate in the firs... | We have geometric series: total over 3 periods = 847. Let first ship have x people, second 2x, third 4x. Sum = x + 2x + 4x =7x =847 => x = 847/7 =121. So first hundred years ship had 121 people. | **Step‑by‑step solution**
1. Let the number of people on the first ship be \(x\).
2. Each subsequent ship has twice as many people as the previous one, so the numbers are:
- 1st ship: \(x\)
- 2nd ship: \(2x\)
- 3rd ship: \(4x\)
3. The monster ate three ships over three hundred years, and the total number of p... | 121 |
gsm8k-train-10-3 | 10 | A deep-sea monster rises from the waters once every hundred years to feast on a ship and sate its hunger. Over three hundred years, it has consumed 847 people. Ships have been built larger over time, so each new ship has twice as many people as the last ship. How many people were on the ship the monster ate in the firs... | We have geometric series. Total people eaten over 300 years = sum of three ships (since every 100 years). Let first ship have x people. Next ship double: 2x, then 4x. Total = x+2x+4x =7x =847. So x =847/7 =121. So first ship had 121 people. | **Step‑by‑step solution**
1. Let the number of people on the first ship be \(x\).
2. Each subsequent ship has twice as many people as the previous one, so the second ship has \(2x\) people and the third ship has \(4x\) people.
3. Over three hundred years the monster ate the crews of three ships, so the total number of... | 121 |
gsm8k-train-10-4 | 10 | A deep-sea monster rises from the waters once every hundred years to feast on a ship and sate its hunger. Over three hundred years, it has consumed 847 people. Ships have been built larger over time, so each new ship has twice as many people as the last ship. How many people were on the ship the monster ate in the firs... | We have geometric series. Over 3 periods (300 years) total consumed 847. Ships sizes: first ship size = x, second = 2x, third = 4x. Sum = x+2x+4x =7x = 847 => x = 847/7 =121. So first ship had 121 people. | The monster eats one ship every hundred years.
Let the number of people on the first ship be \(x\).
Because each later ship has twice as many people as the previous one:
- 1st ship: \(x\) people
- 2nd ship: \(2x\) people
- 3rd ship: \(4x\) people
Over three hundred years the total number of people eaten is
... | 121 |
gsm8k-train-11-0 | 11 | Tobias is buying a new pair of shoes that costs $95. He has been saving up his money each month for the past three months. He gets a $5 allowance a month. He also mows lawns and shovels driveways. He charges $15 to mow a lawn and $7 to shovel. After buying the shoes, he has $15 in change. If he mows 4 lawns, how many d... | We set total saved = 3 months allowance 5 each =15 plus earnings from mowing 4 lawns at 15 each =60 plus x driveways at 7 each =7x. Total =15+60+7x =75+7x. He buys shoes 95 and has 15 left, so total before purchase =95+15=110. So 75+7x =110 =>7x=35 =>x=5. | **Step‑by‑step solution**
1. **Allowance saved:**
Tobias receives \$5 each month for 3 months.
\(3 \times 5 = \$15\)
2. **Earnings from mowing lawns:**
He mows 4 lawns at \$15 each.
\(4 \times 15 = \$60\)
3. **Earnings from shoveling driveways:**
Let the number of driveways he shovels be \(d... | 5 |
gsm8k-train-11-1 | 11 | Tobias is buying a new pair of shoes that costs $95. He has been saving up his money each month for the past three months. He gets a $5 allowance a month. He also mows lawns and shovels driveways. He charges $15 to mow a lawn and $7 to shovel. After buying the shoes, he has $15 in change. If he mows 4 lawns, how many d... | We set up total earnings: allowance 5 per month for 3 months =15. Plus mowing 4 lawns at $15 each =60. Plus shoveling d driveways at $7 each =7d. Total money =15+60+7d =75+7d. He buys shoes 95, left with 15 change, so total before purchase =95+15=110. So 75+7d =110 =>7d=35 => d=5. | **Step‑by‑step solution**
1. **Allowance:**
Tobias gets \$5 each month for 3 months.
\(5 \times 3 = \$15\)
2. **Money from mowing lawns:**
He mows 4 lawns at \$15 each.
\(4 \times 15 = \$60\)
3. **Money from shoveling driveways:**
Let the number of driveways he shovels be \(d\).
Earning... | 5 |
gsm8k-train-11-2 | 11 | Tobias is buying a new pair of shoes that costs $95. He has been saving up his money each month for the past three months. He gets a $5 allowance a month. He also mows lawns and shovels driveways. He charges $15 to mow a lawn and $7 to shovel. After buying the shoes, he has $15 in change. If he mows 4 lawns, how many d... | We set up total savings: allowance 5 per month for 3 months = 15. Plus earnings from mowing and shoveling. Let number of driveways = d. He mowed 4 lawns: 4*15 =60. Shoveling: d*7. Total money = 15 + 60 + 7d. He buys shoes 95, left with 15 change. So total - 95 = 15 => total = 110. So 15+60+7d =110 => 75+7d=110 => 7d=35... | Step 1: Calculate the money from his allowance.
- $5 per month for 3 months → $5 × 3 = $15.
Step 2: Calculate the money from mowing lawns.
- He mows 4 lawns at $15 each → $15 × 4 = $60.
Step 3: Let the number of driveways he shovels be \(d\).
- Money from shoveling → $7 × \(d\).
Step 4: Write the total amount ... | 5 |
gsm8k-train-11-3 | 11 | Tobias is buying a new pair of shoes that costs $95. He has been saving up his money each month for the past three months. He gets a $5 allowance a month. He also mows lawns and shovels driveways. He charges $15 to mow a lawn and $7 to shovel. After buying the shoes, he has $15 in change. If he mows 4 lawns, how many d... | We set up total saved = allowance*3 = 5*3=15 plus earnings from mowing and shoveling. Let number of driveways = d. He mowed 4 lawns => earnings = 4*15 =60. Shoveling earnings = d*7. Total money = 15 + 60 + 7d = 75 + 7d. He buys shoes 95, left with 15 change: So total -95 =15 => total =110. So 75+7d=110 =>7d=35 => d=5. | **Step‑by‑step solution**
1. **Allowance saved:**
Tobias receives a \$5 allowance each month for 3 months.
\(5 \times 3 = \$15\).
2. **Earnings from mowing lawns:**
He mows 4 lawns at \$15 each.
\(4 \times 15 = \$60\).
3. **Earnings from shoveling driveways:**
Let the number of driveways he ... | 5 |
gsm8k-train-11-4 | 11 | Tobias is buying a new pair of shoes that costs $95. He has been saving up his money each month for the past three months. He gets a $5 allowance a month. He also mows lawns and shovels driveways. He charges $15 to mow a lawn and $7 to shovel. After buying the shoes, he has $15 in change. If he mows 4 lawns, how many d... | We set up total earnings: allowance 5 per month for 3 months =15. Plus mowing 4 lawns at $15 each =60. Plus shoveling d driveways at $7 each =7d. Total money =15+60+7d =75+7d. He buys shoes $95 and has $15 left, so he spent 95 and left 15, meaning total was 95+15=110. So 75+7d=110 =>7d=35 => d=5. | **Step‑by‑step solution**
1. **Allowance:**
Tobias receives \$5 each month for 3 months.
\[
5 \times 3 = \$15
\]
2. **Mowing lawns:**
He mows 4 lawns at \$15 each.
\[
4 \times 15 = \$60
\]
3. **Shoveling driveways:**
Let the number of driveways he shovels be \(d\). Each driveway ... | 5 |
gsm8k-train-12-0 | 12 | Randy has 60 mango trees on his farm. He also has 5 less than half as many coconut trees as mango trees. How many trees does Randy have in all on his farm? | We compute coconut trees = (1/2 * mango) -5? "5 less than half as many coconut trees as mango trees" means half as many coconut trees as mango trees, then 5 less than that. So half of mango = 30, then 5 less = 25 coconut trees. Total = 60+25=85. | **Step‑by‑step solution**
1. Randy has **60 mango trees**.
2. He has “5 less than half as many coconut trees as mango trees.”
- Half of the mango trees: \(\frac{1}{2}\times 60 = 30\).
- “5 less than” this number: \(30 - 5 = 25\).
So Randy has **25 coconut trees**.
3. Total number of trees on the farm:... | 85 |
gsm8k-train-12-1 | 12 | Randy has 60 mango trees on his farm. He also has 5 less than half as many coconut trees as mango trees. How many trees does Randy have in all on his farm? | We compute half of mango trees: 60/2 =30. 5 less than that: 30 -5 =25 coconut trees. Total trees =60+25=85. | **Step 1: Find half the number of mango trees**
Half of 60 mango trees is
\[
\frac{60}{2}=30.
\]
**Step 2: Determine the number of coconut trees**
Randy has 5 fewer than this amount, so
\[
30-5 = 25 \text{ coconut trees}.
\]
**Step 3: Add the mango and coconut trees together**
\[
60 \text{ (mango)} + 25 \te... | 85 |
gsm8k-train-12-2 | 12 | Randy has 60 mango trees on his farm. He also has 5 less than half as many coconut trees as mango trees. How many trees does Randy have in all on his farm? | We compute half of mango trees: 60/2=30. 5 less than that: 30-5=25 coconut trees. Total trees = 60+25=85. | **Step‑by‑step solution**
1. Randy has 60 mango trees.
2. Half of the mango trees is
\[
\frac{60}{2}=30.
\]
3. He has 5 fewer coconut trees than this half, so the number of coconut trees is
\[
30-5 = 25.
\]
4. The total number of trees on the farm is the sum of mango and coconut trees:
\[
60 + 25 = 85.
\]
**F... | 85 |
gsm8k-train-12-3 | 12 | Randy has 60 mango trees on his farm. He also has 5 less than half as many coconut trees as mango trees. How many trees does Randy have in all on his farm? | We compute: mango =60. Coconut = half of mango minus 5? "5 less than half as many coconut trees as mango trees" Means: half as many coconut trees as mango trees, then 5 less than that number. So half of mango =30, then 5 less =25 coconut trees. Total =85. | **Step‑by‑step solution**
1. Randy has \(60\) mango trees.
2. “Half as many coconut trees as mango trees” would be \(\frac{1}{2}\times 60 = 30\) coconut trees.
3. He has **5 less** than that number, so the number of coconut trees is
\(30 - 5 = 25\).
4. Total number of trees on the farm = mango trees + cocon... | 85 |
gsm8k-train-12-4 | 12 | Randy has 60 mango trees on his farm. He also has 5 less than half as many coconut trees as mango trees. How many trees does Randy have in all on his farm? | We compute half of mango trees: 60/2 =30. 5 less than that: 30 -5 =25 coconut trees. Total trees =60+25=85. | **Step‑by‑step solution**
1. Randy has 60 mango trees.
2. Half of the number of mango trees is
\[
\frac{60}{2}=30.
\]
3. He has 5 fewer coconut trees than this half, so the number of coconut trees is
\[
30-5=25.
\]
4. The total number of trees on the farm is the sum of mango and coconut tre... | 85 |
gsm8k-train-14-0 | 14 | Joy can read 8 pages of a book in 20 minutes. How many hours will it take her to read 120 pages? | We compute rate: 8 pages per 20 min = 0.4 pages per minute. For 120 pages need 120 / 0.4 = 300 minutes. Convert to hours: 300/60 = 5 hours. | **Step 1: Determine Joy’s reading rate**
Joy reads 8 pages in 20 minutes.
\[
\text{Reading rate} = \frac{8\text{ pages}}{20\text{ min}} = \frac{8}{20}\text{ pages/min} = 0.4\text{ pages/min}
\]
**Step 2: Find the time needed for 120 pages**
\[
\text{Time (minutes)} = \frac{\text{Number of pages}}{\text{Rate}} = \fr... | 5 |
gsm8k-train-14-1 | 14 | Joy can read 8 pages of a book in 20 minutes. How many hours will it take her to read 120 pages? | We compute rate: 8 pages per 20 min => 0.4 pages per minute. For 120 pages: 120 / 0.4 = 300 minutes. Convert to hours: 300/60 = 5 hours. | **Step 1: Find Joy’s reading rate**
Joy reads 8 pages in 20 minutes.
\[
\text{Rate} = \frac{8\text{ pages}}{20\text{ min}} = 0.4\text{ pages per minute}
\]
**Step 2: Determine the time needed for 120 pages**
\[
\text{Time (minutes)} = \frac{120\text{ pages}}{0.4\text{ pages/min}} = 300\text{ minutes}
\]
**Step 3: ... | 5 |
gsm8k-train-14-2 | 14 | Joy can read 8 pages of a book in 20 minutes. How many hours will it take her to read 120 pages? | We compute rate: 8 pages per 20 min => 0.4 pages per minute. For 120 pages need 120 / 0.4 = 300 minutes. Convert to hours: 300/60 = 5 hours. | **Step 1: Determine Joy’s reading rate**
- Joy reads 8 pages in 20 minutes.
- Rate = \(\frac{8\text{ pages}}{20\text{ min}} = 0.4\text{ pages per minute}\).
**Step 2: Find the time needed for 120 pages**
- Time (in minutes) = \(\frac{\text{pages}}{\text{rate}} = \frac{120\text{ pages}}{0.4\text{ pages/min}} = 300\... | 5 |
gsm8k-train-14-3 | 14 | Joy can read 8 pages of a book in 20 minutes. How many hours will it take her to read 120 pages? | Compute rate: 8 pages per 20 min = 0.4 pages per min. For 120 pages: 120 /0.4 = 300 minutes = 5 hours. | **Step 1: Find Joy’s reading rate**
- Joy reads 8 pages in 20 minutes.
- Reading rate = \( \frac{8\text{ pages}}{20\text{ minutes}} = 0.4\text{ pages per minute} \).
**Step 2: Determine the time needed for 120 pages**
- Time (minutes) = \( \frac{\text{pages}}{\text{rate}} = \frac{120\text{ pages}}{0.4\text{ pages/... | 5 |
gsm8k-train-14-4 | 14 | Joy can read 8 pages of a book in 20 minutes. How many hours will it take her to read 120 pages? | We compute rate: 8 pages per 20 min = 0.4 pages per min. For 120 pages need 120 / 0.4 = 300 minutes. Convert to hours: 300/60 = 5 hours. | **Step 1: Find Joy’s reading rate**
Joy reads 8 pages in 20 minutes.
Reading rate = \(\frac{8\text{ pages}}{20\text{ min}} = 0.4\text{ pages per minute}\).
**Step 2: Determine the time needed for 120 pages**
Time (in minutes) = \(\frac{\text{total pages}}{\text{rate}} = \frac{120\text{ pages}}{0.4\text{ pages/min}... | 5 |
gsm8k-train-15-0 | 15 | James creates a media empire. He creates a movie for $2000. Each DVD cost $6 to make. He sells it for 2.5 times that much. He sells 500 movies a day for 5 days a week. How much profit does he make in 20 weeks? | We compute profit per DVD: cost to make DVD = $6. Selling price = 2.5 * 6 = $15. So profit per DVD = 15 - 6 = $9. Also initial movie creation cost $2000 one-time.
He sells 500 movies a day, 5 days a week => 500*5 = 2500 per week. Over 20 weeks: 2500*20 = 50,000 DVDs sold.
Profit from sales = 50,000 * $9 = $450,000.
... | **Step 1: Determine the selling price of each DVD**
- Cost to make each DVD = \$6
- Selling price = 2.5 × \$6 = **\$15**
**Step 2: Compute profit per DVD**
- Profit per DVD = Selling price – Cost = \$15 – \$6 = **\$9**
**Step 3: Find the number of DVDs sold in 20 weeks**
- DVDs sold per day = 500
- Days sol... | 448000 |
gsm8k-train-15-1 | 15 | James creates a media empire. He creates a movie for $2000. Each DVD cost $6 to make. He sells it for 2.5 times that much. He sells 500 movies a day for 5 days a week. How much profit does he make in 20 weeks? | Compute profit per DVD: cost =6, sell price =2.5*6=15. Profit per DVD =9. Also movie creation cost $2000 one-time. Daily sold 500 DVDs, 5 days a week => 2500 per week. Profit per week =2500*9 =22500. Over 20 weeks profit =22500*20=450,000. Subtract initial $2000? Already accounted? The $2000 is cost to create movie, sh... | **Step 1: Determine the selling price of one DVD**
- Cost to make one DVD = \$6
- Selling price = 2.5 × \$6 = \$15
**Step 2: Find the profit per DVD**
- Profit per DVD = Selling price – Cost = \$15 – \$6 = **\$9**
**Step 3: Calculate how many DVDs are sold each week**
- DVDs sold per day = 500
- Days sold... | 448000 |
gsm8k-train-15-2 | 15 | James creates a media empire. He creates a movie for $2000. Each DVD cost $6 to make. He sells it for 2.5 times that much. He sells 500 movies a day for 5 days a week. How much profit does he make in 20 weeks? | We compute profit per DVD: cost $6, selling price = 2.5 * 6 = $15. So profit per DVD = 15 - 6 = $9. Also there is a fixed movie creation cost $2000 (maybe one-time). He sells 500 movies a day, 5 days a week => 500*5 = 2500 per week. Over 20 weeks: 2500*20 = 50,000 DVDs sold. Total profit from sales = 50,000 * $9 = $450... | **Step‑by‑step solution**
1. **Cost to make each DVD:** \$6
2. **Selling price per DVD:** \(2.5 \times 6 = \$15\)
3. **Profit per DVD:** \(15 - 6 = \$9\)
4. **Number of DVDs sold per day:** 500
**Days sold per week:** 5
**DVDs sold per week:** \(500 \times 5 = 2{,}500\)
5. **Number of weeks:** 20
... | 448000 |
gsm8k-train-15-3 | 15 | James creates a media empire. He creates a movie for $2000. Each DVD cost $6 to make. He sells it for 2.5 times that much. He sells 500 movies a day for 5 days a week. How much profit does he make in 20 weeks? | We compute profit per DVD: cost $6, sells for 2.5*6 = $15. So profit per DVD = 15-6 = $9. Also initial movie creation cost $2000 (one-time). He sells 500 movies a day, 5 days a week => 500*5 = 2500 per week. Over 20 weeks: 2500*20 = 50,000 DVDs sold. Profit from sales = 50,000 * $9 = $450,000. Subtract initial cost $20... | **Step‑by‑step solution**
1. **Cost to make each DVD** = \$6.
2. **Selling price** = 2.5 × \$6 = \$15.
3. **Profit per DVD** = \$15 – \$6 = **\$9**.
4. **Number of DVDs sold per day** = 500.
5. **Days sold per week** = 5 → DVDs sold per week = 500 × 5 = **2 500**.
6. **Number of weeks** = 20 → total DVDs sold ... | 448000 |
gsm8k-train-15-4 | 15 | James creates a media empire. He creates a movie for $2000. Each DVD cost $6 to make. He sells it for 2.5 times that much. He sells 500 movies a day for 5 days a week. How much profit does he make in 20 weeks? | We compute profit per DVD: cost = $6, selling price = 2.5*6 = $15. So profit per DVD = 15-6 = $9. Also initial movie creation cost $2000 (one-time). He sells 500 movies a day, 5 days a week => 500*5 = 2500 per week. Over 20 weeks => 2500*20 = 50,000 DVDs sold. Total profit from sales = 50,000 * $9 = $450,000. Subtract ... | **Step‑by‑step calculation**
1. **Cost to produce each DVD:** \$6
2. **Selling price of each DVD:** \(2.5 \times 6 = \$15\)
3. **Profit per DVD:** \(15 - 6 = \$9\)
4. **DVDs sold per day:** 500
**Days sold per week:** 5
**DVDs sold per week:** \(500 \times 5 = 2{,}500\)
5. **DVDs sold in 20 weeks:** \(... | 448000 |
gsm8k-train-16-0 | 16 | The profit from a business transaction is shared among 2 business partners, Mike and Johnson in the ratio 2:5 respectively. If Johnson got $2500, how much will Mike have after spending some of his share on a shirt that costs $200? | We need total ratio 2:5, Johnson got 2500 corresponds to 5 parts. One part = 2500/5 = 500. Mike gets 2 parts = 1000. Then Mike spends 200 on shirt, remaining = 800. Final answer 800. | **Step 1: Determine the value of one part of the ratio**
The profit is divided in the ratio \(2:5\) (Mike : Johnson).
Johnson’s share corresponds to the 5 parts and equals \$2500.
\[
\text{Value of one part} = \frac{2500}{5}= \$500
\]
**Step 2: Find Mike’s original share**
Mike’s share corresponds to the 2 part... | 800 |
gsm8k-train-16-1 | 16 | The profit from a business transaction is shared among 2 business partners, Mike and Johnson in the ratio 2:5 respectively. If Johnson got $2500, how much will Mike have after spending some of his share on a shirt that costs $200? | We compute total ratio parts =7. Johnson got 2500 corresponds to 5 parts, so one part = 2500/5 = 500. Mike gets 2 parts = 1000. He spends $200 on shirt, remaining = 800. Provide steps. | **Step 1: Set up the ratio**
The profit is divided in the ratio
\[
\text{Mike} : \text{Johnson}= 2:5
\]
Let one “part” of the ratio be worth \(x\) dollars. Then
\[
\begin{aligned}
\text{Mike’s share} &= 2x \\
\text{Johnson’s share} &= 5x
\end{aligned}
\]
**Step 2: Find the value of one part**
Johnson received... | 800 |
gsm8k-train-16-2 | 16 | The profit from a business transaction is shared among 2 business partners, Mike and Johnson in the ratio 2:5 respectively. If Johnson got $2500, how much will Mike have after spending some of his share on a shirt that costs $200? | We compute total parts =2+5=7. Johnson's share =5 parts = $2500, so one part = 2500/5 = 500. Mike's share =2 parts = 2*500 = $1000. He spends $200, remaining = 800. Provide steps. | **Step 1: Determine the value of one part of the ratio**
The profit is divided in the ratio \(2:5\).
Total parts = \(2 + 5 = 7\).
Johnson’s share corresponds to 5 parts and is given as \$2500.
\[
\text{Value of one part} = \frac{\$2500}{5} = \$500
\]
**Step 2: Find Mike’s original share**
Mike’s share corresp... | 800 |
gsm8k-train-16-3 | 16 | The profit from a business transaction is shared among 2 business partners, Mike and Johnson in the ratio 2:5 respectively. If Johnson got $2500, how much will Mike have after spending some of his share on a shirt that costs $200? | We compute total ratio 2+5=7 parts. Johnson 5 parts = $2500, so one part = 2500/5 = 500. Mike gets 2 parts = 2*500 = $1000. He spends $200, left = 800. Provide steps. | **Step 1: Find the value of one part of the ratio**
The profit is divided in the ratio \(2:5\) (Mike : Johnson).
Total number of parts = \(2 + 5 = 7\).
Johnson’s share corresponds to 5 parts and is given as \$2500.
\[
\text{Value of one part} = \frac{\$2500}{5}= \$500
\]
**Step 2: Compute Mike’s original share**
... | 800 |
gsm8k-train-16-4 | 16 | The profit from a business transaction is shared among 2 business partners, Mike and Johnson in the ratio 2:5 respectively. If Johnson got $2500, how much will Mike have after spending some of his share on a shirt that costs $200? | We compute total ratio 2+5=7 parts. Johnson's share =5 parts = $2500 so one part = 2500/5 = 500. Mike's share =2 parts = 2*500 = $1000. He spends $200, remaining = 800. | **Step 1: Determine the value of one part of the ratio**
The profit is divided in the ratio \(2:5\).
Total number of parts = \(2 + 5 = 7\).
Johnson receives the 5‑part share, which is given as \$2500.
\[
\text{Value of one part} = \frac{\$2500}{5} = \$500
\]
**Step 2: Find Mike’s original share**
Mike receive... | 800 |
gsm8k-train-17-0 | 17 | In a truck, there are 26 pink hard hats, 15 green hard hats, and 24 yellow hard hats. If Carl takes away 4 pink hard hats, and John takes away 6 pink hard hats and twice as many green hard hats as the number of pink hard hats that he removed, then calculate the total number of hard hats that remained in the truck. | We compute initial total = 26+15+24=65. Carl removes 4 pink. John removes 6 pink and twice as many green as pink he removed: pink removed by John =6, so green removed = 2*6=12. Total removed = Carl 4 pink + John 6 pink +12 green =22 hats. No yellow removed. Remaining =65-22=43. | **Step 1: Find the initial total number of hard hats.**
- Pink: 26
- Green: 15
- Yellow: 24
Total initially
\(26 + 15 + 24 = 65\) hats.
**Step 2: Determine how many hats each person removes.**
- Carl removes 4 pink hats.
- John removes 6 pink hats.
He also removes twice as many green hats as the p... | 43 |
gsm8k-train-17-1 | 17 | In a truck, there are 26 pink hard hats, 15 green hard hats, and 24 yellow hard hats. If Carl takes away 4 pink hard hats, and John takes away 6 pink hard hats and twice as many green hard hats as the number of pink hard hats that he removed, then calculate the total number of hard hats that remained in the truck. | We compute initial total: 26+15+24=65. Carl removes 4 pink. John removes 6 pink and twice as many green as pink he removed: pink removed by John =6, so green removed =2*6=12. No yellow removed. Total removed =4+6 pink =10 pink removed, plus 12 green =22 removed. Remaining hats: pink left =26-10=16. Green left =15-12=3.... | **Step‑by‑step solution**
1. **Initial numbers of hard hats**
- Pink: 26
- Green: 15
- Yellow: 24
Total initially = \(26 + 15 + 24 = 65\).
2. **Hats taken by Carl**
- Carl takes away 4 pink hats.
3. **Hats taken by John**
- John takes away 6 pink hats.
- He also takes away twice as many g... | 43 |
gsm8k-train-17-2 | 17 | In a truck, there are 26 pink hard hats, 15 green hard hats, and 24 yellow hard hats. If Carl takes away 4 pink hard hats, and John takes away 6 pink hard hats and twice as many green hard hats as the number of pink hard hats that he removed, then calculate the total number of hard hats that remained in the truck. | We compute initial total: 26+15+24=65. Carl takes 4 pink => pink left 22. John takes 6 pink and twice as many green as pink he removed: pink removed 6, so green removed = 2*6=12. So John removes 6 pink, 12 green. After Carl and John, pink removed total =4+6=10, so pink left =26-10=16. Green removed =12, so green left =... | **Step‑by‑step solution**
1. **Initial counts**
- Pink hats: 26
- Green hats: 15
- Yellow hats: 24
Total initially = \(26 + 15 + 24 = 65\).
2. **Carl’s removal**
- Carl takes away 4 pink hats.
- Pink hats left after Carl: \(26 - 4 = 22\).
3. **John’s removal**
- John takes away 6 pink h... | 43 |
gsm8k-train-17-3 | 17 | In a truck, there are 26 pink hard hats, 15 green hard hats, and 24 yellow hard hats. If Carl takes away 4 pink hard hats, and John takes away 6 pink hard hats and twice as many green hard hats as the number of pink hard hats that he removed, then calculate the total number of hard hats that remained in the truck. | We compute initial total: 26+15+24=65. Carl removes 4 pink. John removes 6 pink and twice as many green as pink he removed: pink removed by John =6, so green removed =2*6=12. Total removed: Carl 4 pink, John 6 pink +12 green =18. So total removed =4+6+12=22. Remaining hats =65-22=43. Note yellow unchanged. Final answer... | **Step 1: Find the initial total number of hard hats**
- Pink: 26
- Green: 15
- Yellow: 24
Total initially = 26 + 15 + 24 = **65** hats.
**Step 2: Determine how many hats each person removes**
- Carl removes 4 pink hats.
- John removes 6 pink hats.
- John also removes twice as many green hats as the pin... | 43 |
gsm8k-train-17-4 | 17 | In a truck, there are 26 pink hard hats, 15 green hard hats, and 24 yellow hard hats. If Carl takes away 4 pink hard hats, and John takes away 6 pink hard hats and twice as many green hard hats as the number of pink hard hats that he removed, then calculate the total number of hard hats that remained in the truck. | We compute initial total: 26+15+24=65. Carl removes 4 pink. John removes 6 pink and twice as many green as pink he removed: pink removed by John =6, so green removed =2*6=12. So total removed: Carl 4 pink, John 6 pink +12 green =22 hats. Also John didn't remove yellow. So remaining hats: pink left =26-4-6=16. Green lef... | **Step‑by‑step calculation**
1. **Initial number of hard hats**
- Pink: 26
- Green: 15
- Yellow: 24
Total initially = \(26 + 15 + 24 = 65\).
2. **Hats taken by Carl**
- Carl removes 4 pink hats.
3. **Hats taken by John**
- John removes 6 pink hats.
- He also removes twice as man... | 43 |
gsm8k-train-18-0 | 18 | It takes Roque two hours to walk to work and one hour to ride his bike to work. Roque walks to and from work three times a week and rides his bike to and from work twice a week. How many hours in total does he take to get to and from work a week with walking and biking? | We compute: walking round trip takes 2h each way => 4h per day. He does that 3 times a week (to and from counts as one round trip?). "walks to and from work three times a week" means 3 round trips? Likely 3 days walking round trip. So total walking hours = 4h *3 =12h. Biking: 1h each way =>2h round trip. Does twice a w... | **Step‑by‑step solution**
1. **Walking time**
- One way walking: 2 hours.
- Round‑trip walking (to *and* from work): \(2 \text{h} + 2 \text{h} = 4 \text{h}\).
- He walks round‑trip **3 times** a week: \(4 \text{h} \times 3 = 12 \text{h}\).
2. **Biking time**
- One way biking: 1 hour.
- Round‑... | 16 |
gsm8k-train-18-1 | 18 | It takes Roque two hours to walk to work and one hour to ride his bike to work. Roque walks to and from work three times a week and rides his bike to and from work twice a week. How many hours in total does he take to get to and from work a week with walking and biking? | We compute round trips. Walking: 2 hours one way, so round trip 4 hours. He does that 3 times a week (to and from). So 3 * 4 = 12 hours. Biking: 1 hour one way, round trip 2 hours. He does that 2 times a week. So 2 * 2 = 4 hours. Total = 12 + 4 = 16 hours. | **Step‑by‑step solution**
1. **Walking:**
- One‑way walking time = 2 hours.
- A round trip (to *and* from work) = \(2 \text{ h} + 2 \text{ h} = 4\) hours.
- He walks round trips 3 times per week, so walking time per week = \(3 \times 4 = 12\) hours.
2. **Biking:**
- One‑way biking time = 1 hour. ... | 16 |
gsm8k-train-18-2 | 18 | It takes Roque two hours to walk to work and one hour to ride his bike to work. Roque walks to and from work three times a week and rides his bike to and from work twice a week. How many hours in total does he take to get to and from work a week with walking and biking? | We need total hours for round trips. Walking: 2 hours one way, so round trip = 4 hours. He does walking to and from three times a week meaning three round trips? "walks to and from work three times a week" likely means three days walking both ways, so 3 round trips. So walking total = 3 * 4 = 12 hours. Biking: 1 hour o... | **Step‑by‑step solution**
1. **Walking:**
- One‑way walking time = 2 hours.
- Round‑trip walking time = 2 h + 2 h = 4 hours.
- He walks to and from work **3 times** per week → 3 round trips.
- Total walking time per week = 3 × 4 h = **12 hours**.
2. **Biking:**
- One‑way biking time = 1 hour.... | 16 |
gsm8k-train-18-3 | 18 | It takes Roque two hours to walk to work and one hour to ride his bike to work. Roque walks to and from work three times a week and rides his bike to and from work twice a week. How many hours in total does he take to get to and from work a week with walking and biking? | We compute: walking round trip takes 2h each way? It says two hours to walk to work (one way). So round trip walking = 4h. He walks to and from work three times a week => that's three round trips? "walks to and from work three times a week" means three days he walks both ways. So total walking hours = 3 * 4 = 12h.
Bik... | **Step‑by‑step solution**
1. **Walking time**
- One‑way walk: 2 hours
- Round‑trip walk: \(2 \text{ h} \times 2 = 4\) hours
- He walks round‑trip 3 times a week: \(4 \text{ h} \times 3 = 12\) hours
2. **Biking time**
- One‑way bike ride: 1 hour
- Round‑trip bike ride: \(1 \text{ h} \times 2 = 2\)... | 16 |
gsm8k-train-18-4 | 18 | It takes Roque two hours to walk to work and one hour to ride his bike to work. Roque walks to and from work three times a week and rides his bike to and from work twice a week. How many hours in total does he take to get to and from work a week with walking and biking? | We compute: walking round trip takes 2h each way so 4h per day. He does that 3 times a week (to and from?), wording: walks to and from work three times a week meaning three round trips? Likely three days walking both ways. So 3 * 4 =12h. Biking round trip: 1h each way =2h per day. Does twice a week: 2*2=4h. Total 16h. | **Step‑by‑step solution**
1. **Walking**
- Time to walk **one way** to work: 2 hours.
- Time to walk **back** from work: another 2 hours.
- So a **round‑trip** walking day takes \(2 + 2 = 4\) hours.
- Roque walks to and from work **three times a week** (i.e., three round‑trip days).
- Total wa... | 16 |
gsm8k-train-19-0 | 19 | Tim rides his bike back and forth to work for each of his 5 workdays. His work is 20 miles away. He also goes for a weekend bike ride of 200 miles. If he can bike at 25 mph how much time does he spend biking a week? | We compute: each workday round trip = 20 miles each way? Actually work is 20 miles away, so round trip is 40 miles per day. 5 days => 200 miles. Weekend ride 200 miles. Total weekly miles = 400 miles. Speed 25 mph. Time = distance / speed = 400 / 25 = 16 hours. Provide steps. | **Step 1: Determine the distance biked each workday**
- One‑way distance to work = 20 miles
- Round‑trip distance per day = 20 mi × 2 = **40 miles**
**Step 2: Compute total work‑week distance**
- Number of workdays = 5
- Total work‑week distance = 40 mi/day × 5 days = **200 miles**
**Step 3: Add the weekend r... | 16 |
gsm8k-train-19-1 | 19 | Tim rides his bike back and forth to work for each of his 5 workdays. His work is 20 miles away. He also goes for a weekend bike ride of 200 miles. If he can bike at 25 mph how much time does he spend biking a week? | We compute: each workday round trip = 20 miles each way? Actually work is 20 miles away, so round trip 40 miles per day. 5 days => 200 miles. Weekend ride 200 miles. Total 400 miles. Speed 25 mph => time = 400/25 = 16 hours. | **Step‑by‑step solution**
1. **Distance to work each way:** 20 mi
**Round‑trip distance per workday:** \(20 \text{ mi} \times 2 = 40 \text{ mi}\)
2. **Total work‑day biking distance:**
\(40 \text{ mi/day} \times 5 \text{ days} = 200 \text{ mi}\)
3. **Weekend bike ride distance:** 200 mi
4. **Total weekl... | 16 |
gsm8k-train-19-2 | 19 | Tim rides his bike back and forth to work for each of his 5 workdays. His work is 20 miles away. He also goes for a weekend bike ride of 200 miles. If he can bike at 25 mph how much time does he spend biking a week? | We compute: each workday round trip = 20 miles each way? Actually work is 20 miles away, so round trip = 40 miles per day. 5 days => 200 miles. Weekend ride 200 miles. Total miles = 400 miles. Speed 25 mph. Time = 400/25 = 16 hours. | **Step‑by‑step solution**
1. **Distance for the daily commute**
- Work is 20 mi away, so a round‑trip each day is \(20 \text{ mi} \times 2 = 40 \text{ mi}\).
- He commutes 5 days a week: \(40 \text{ mi/day} \times 5 \text{ days} = 200 \text{ mi}\).
2. **Weekend bike ride**
- The weekend ride adds anoth... | 16 |
gsm8k-train-19-3 | 19 | Tim rides his bike back and forth to work for each of his 5 workdays. His work is 20 miles away. He also goes for a weekend bike ride of 200 miles. If he can bike at 25 mph how much time does he spend biking a week? | We calculate: daily commute: 20 miles each way? "back and forth to work" means round trip 40 miles per day. 5 workdays => 5 * 40 = 200 miles. Weekend ride 200 miles. Total weekly miles = 400 miles. Speed 25 mph, time = distance/speed = 400/25 = 16 hours. | **Step 1: Determine the distance biked each workday**
- One way to work = 20 miles
- Round‑trip each day = 20 mi × 2 = **40 miles**
**Step 2: Compute total distance for the 5 workdays**
- 40 miles/day × 5 days = **200 miles**
**Step 3: Add the weekend ride**
- Weekend ride = **200 miles**
- Total weekly dis... | 16 |
gsm8k-train-19-4 | 19 | Tim rides his bike back and forth to work for each of his 5 workdays. His work is 20 miles away. He also goes for a weekend bike ride of 200 miles. If he can bike at 25 mph how much time does he spend biking a week? | We calculate: each workday round trip = 20 miles each way? Actually work is 20 miles away, so round trip is 40 miles per day. 5 days => 200 miles. Weekend ride 200 miles. Total = 400 miles. Speed 25 mph => time = 400/25 = 16 hours. | **Step 1: Determine the distance biked each workday**
- Distance from home to work = 20 mi
- He rides to work and back, so each day he bikes \(20 mi \times 2 = 40 mi\).
**Step 2: Compute total work‑day distance for the week**
- He works 5 days a week.
- Total work‑day mileage = \(40 mi \times 5 = 200 mi\).
**... | 16 |
gsm8k-train-21-0 | 21 | Each bird eats 12 beetles per day, each snake eats 3 birds per day, and each jaguar eats 5 snakes per day. If there are 6 jaguars in a forest, how many beetles are eaten each day? | We calculate: 6 jaguars each eat 5 snakes => 30 snakes. Each snake eats 3 birds => 30*3=90 birds. Each bird eats 12 beetles => 90*12 = 1080 beetles. | **Step‑by‑step solution**
1. **Jaguars → snakes**
Each jaguar eats 5 snakes.
With 6 jaguars: \(6 \times 5 = 30\) snakes are eaten.
2. **Snakes → birds**
Each snake eats 3 birds.
With 30 snakes: \(30 \times 3 = 90\) birds are eaten.
3. **Birds → beetles**
Each bird eats 12 beetles.
With ... | 1080 |
gsm8k-train-21-1 | 21 | Each bird eats 12 beetles per day, each snake eats 3 birds per day, and each jaguar eats 5 snakes per day. If there are 6 jaguars in a forest, how many beetles are eaten each day? | We compute: 6 jaguars eat 5 snakes each => 30 snakes. Each snake eats 3 birds => 30*3 = 90 birds. Each bird eats 12 beetles => 90*12 = 1080 beetles. | **Step‑by‑step solution**
1. **Jaguars → snakes**
Each jaguar eats 5 snakes per day.
With 6 jaguars:
\[
6 \text{ jaguars} \times 5 \frac{\text{snakes}}{\text{jaguar}} = 30 \text{ snakes}
\]
2. **Snakes → birds**
Each snake eats 3 birds per day.
With 30 snakes:
\[
30 \text{ snake... | 1080 |
gsm8k-train-21-2 | 21 | Each bird eats 12 beetles per day, each snake eats 3 birds per day, and each jaguar eats 5 snakes per day. If there are 6 jaguars in a forest, how many beetles are eaten each day? | We compute: 6 jaguars each eat 5 snakes => total snakes eaten = 6*5 =30 snakes per day. Each snake eats 3 birds => total birds eaten = 30*3 =90 birds per day. Each bird eats 12 beetles => beetles eaten = 90*12 =1080. So final answer 1080. | **Step‑by‑step solution**
1. **Jaguars → snakes**
Each jaguar eats 5 snakes.
With 6 jaguars:
\(6 \times 5 = 30\) snakes are eaten each day.
2. **Snakes → birds**
Each snake eats 3 birds.
With 30 snakes:
\(30 \times 3 = 90\) birds are eaten each day.
3. **Birds → beetles**
Each bird... | 1080 |
gsm8k-train-21-3 | 21 | Each bird eats 12 beetles per day, each snake eats 3 birds per day, and each jaguar eats 5 snakes per day. If there are 6 jaguars in a forest, how many beetles are eaten each day? | We compute: 6 jaguars eat 5 snakes each => 6*5=30 snakes. Each snake eats 3 birds => 30*3=90 birds. Each bird eats 12 beetles => 90*12 = 1080 beetles. | **Step‑by‑step solution**
1. **Jaguars to snakes**
Each jaguar eats 5 snakes.
With 6 jaguars:
\[
6 \text{ jaguars} \times 5 \frac{\text{snakes}}{\text{jaguar}} = 30 \text{ snakes}
\]
2. **Snakes to birds**
Each snake eats 3 birds.
With 30 snakes:
\[
30 \text{ snakes} \times 3 \f... | 1080 |
gsm8k-train-22-0 | 22 | Samantha’s last name has three fewer letters than Bobbie’s last name. If Bobbie took two letters off her last name, she would have a last name twice the length of Jamie’s. Jamie’s full name is Jamie Grey. How many letters are in Samantha’s last name? | We need unknown lengths. Let S = length of Samantha's last name. B = length of Bobbie's last name. Given S = B - 3. If Bobbie took two letters off her last name, she would have a last name twice the length of Jamie’s. Jamie’s full name is Jamie Grey. So Jamie's last name "Grey" length = 4. So after removing 2 letters, ... | Let
- \(S\) = number of letters in Samantha’s last name
- \(B\) = number of letters in Bobbie’s last name
**Given relationships**
1. Samantha’s last name has three fewer letters than Bobbie’s:
\[
S = B - 3
\]
2. If Bobbie removes two letters from her last name, the remaining length equals twice Jam... | 7 |
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