prompt stringlengths 211 807 | chosen stringlengths 85 13.6k | rejected stringlengths 89 18.3k | answer stringlengths 1 6 |
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You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Mimi picked up 2 dozen seashells on the beach. Kyle found twice as many shells as Mimi and put them in his pocket. Leigh grabbed one-third of the shells that Kyle found. How many seashell... | Step 1: Mimi picked up 2 dozen seashells, which is 24 seashells.
Step 2: Kyle found twice as many shells as Mimi, so Kyle found 2 * 24 = 48 seashells.
Step 3: Leigh grabbed one-third of the shells that Kyle found, so Leigh grabbed 1/3 * 48 = 16 seashells.
Step 4: So Leigh has 16 seashells.
#### 16 | Step 1: Calculate the number of shells Kyle found.
Kyle found twice as many shells as Mimi. 2 * 2 = 4
Step 2: Calculate the number of shells Leigh grabbed from Kyle.
Leigh grabbed one-third of the shells that Kyle found. 1/3 * 4 = 4/3 = 1.33
Step 3: Since you can't have a fraction of a seashell, you can round the numb... | 16 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Ezekiel hikes as a hobby. This past summer, he did a challenging three-day hike across 50 kilometers of wilderness. The first day, he covered 10 kilometers of steep mountainside. The second... | Step 1: Ezekiel covered 10 kilometers on the first day of the hike.
Step 2: Ezekiel covered half of the full hike distance on the second day. Therefore, Ezekiel covered (1/2)*50 kilometers on the second day. This gives a distance of 25 kilometers.
Step 3: The total distance of the hike is 50 kilometers. Ezekiel cove... | Step 1: Let x be the total distance Ezekiel had to hike.
Step 2: Since Ezekiel covered 10 kilometers on the first day, the distance he covered on the second day is half the full hike distance, which is x/2.
Step 3: To find the distance Ezekiel covered on the third day, we can subtract the distance covered on the first ... | 15 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: James decides to build a tin house by collecting 500 tins in a week. On the first day, he collects 50 tins. On the second day, he manages to collect 3 times that number. On the third day, h... | ## Step 1: Determine the number of tins James collected on the second day.
On the second day, James collected 3 times the number of tins he collected on the first day. Since the first day he collected 50 tins, the second day he collected 3 * 50 = 150 tins.
## Step 2: Determine the number of tins James collected on the... | ## Step 1: Calculate the number of tins James collected on the first day.
James collects 50 tins on the first day.
## Step 2: Calculate the number of tins James collected on the second day.
He collects 3 times the number of tins collected on the first day, which is 3 * 50 = 150 tins.
## Step 3: Calculate the number o... | 50 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Don throws 3 darts. One is a bullseye worth 50 points. One completely missed the target, so received no points. The third was worth half the points of the bullseye. What is the final sco... | Step 1: First, we must calculate the total number of points the bullseye is worth. Since one is worth 50 points, the total points from the bullseye is 50.
Step 2: Next, we calculate the points from the other two throws. Since one was worth 0, it is worth 0 points. The third throw was worth half the points of the b... | Step 1: Define variables for each throw.
Let x = points from the bullseye, y = points from the second throw, and z = points from the third throw.
Step 2: Set up equations based on the information given.
We know that:
- x + y + z = 50
- y = 0
- z = 0.5x
Step 3: Substitute y = 0 and z = 0.5x into the equation x + y + z... | 75 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: TreQuan is throwing rocks in the river and he notices that the bigger the rock, the wider the splash. Pebbles make a splash that is a 1/4 meter wide. Rocks make a splash that is 1/2 a meter... | Step 1: First, calculate the total width of the pebble splashes.
Step 2: Next, calculate the total width of the rock splashes.
Step 3: Finally, calculate the total width of the boulder splashes.
Step 4: Add up the widths of the pebble, rock, and boulder splashes to find the total width of the splashes made by TreQuan.
... | First, calculate the width of the splashes made by each object. The width of the pebble splash is 1/4 meter, the width of the rock splash is 1/2 meter, and the width of the boulder splash is 2 meters.
Next, add the width of each type of splash together to get the total width of the splashes made by all the objects.
F... | 7 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Pauly is making omelets for his family. There are three dozen eggs, and he plans to use them all. Each omelet requires 4 eggs. Including himself, there are 3 people. How many omelets does e... | Step 1: Determine how many eggs are used in total. Since there are three dozen eggs, that is 3 * 12 = 36 eggs in total.
Step 2: Determine how many omelets can be made with the total number of eggs. If each omelet requires 4 eggs, then the number of omelets that can be made is 36 / 4 = 9.
Step 3: Since there are 3 pe... | Step 1: First, convert the number of eggs from dozen to individual eggs. Since there are 12 eggs in a dozen, three dozen eggs is three times 12, or 36 eggs.
Step 2: Next, divide the total number of eggs by the number of people to determine how many eggs will be left after making omelets for Pauly and his family. Since ... | 3 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Thomas made 4 stacks of wooden blocks. The first stack was 7 blocks tall. The second stack was 3 blocks taller than the first. The third stack was 6 blocks shorter than the second stack, an... | Step 1: The height of the first stack is 7. Step 2: The height of the second stack is 7 + 3 = 10. Step 3: The height of the third stack is 10 - 6 = 4. Step 4: The height of the fourth stack is 4 + 10 = 14. Step 5: The height of the fifth stack is 2 × 10 = 20. Step 6: The total number of blocks used is 7 + 10 + 4 + 14 +... | Step 1: Write the equation that represents the number of blocks in each stack
Let n = number of blocks in the first stack
Let m = number of blocks in the second stack
Let k = number of blocks in the third stack
Let l = number of blocks in the fourth stack
Let t = number of blocks in the fifth stack
... | 55 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Trace has five shopping bags that weigh the same amount as Gordon’s two shopping bags. One of Gordon’s shopping bags weighs three pounds and the other weighs seven. Trace’s shopping bags al... | Step 1: Let the weights of Trace’s shopping bags be x and y.
Step 2: From the information given, we can set up the following equations: x + y = 3(2) and x + 7 = y. Step 3: We can solve the second equation for y to get y = 2x. Step 4: Substitute this expression into the first equation: x + 2x = 6. Step 5: Combine like t... | Step 1: To solve this problem, let's denote the weight of one of Trace's shopping bags as x pounds.
Step 2: We know that the total weight of Gordon's two bags is the sum of the weights of his two bags. So, Gordon's total weight is 3 + 7 = 10 pounds.
Step 3: Since Trace's five shopping bags all weigh the same amount,... | 2 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: A library has a number of books. 35% of them are intended for children and 104 of them are for adults. How many books are in the library?
Answer:
| Step 1: Let the total number of books be represented by x.
Step 2: Since 35% of the books are for children, 65% must be for adults. This means the number of adult books is 0.65x.
Step 3: We know that the number of adult books is 104, so we can set up the equation 0.65x = 104.
Step 4: Solving for x, we have x = 104 ... | Step 1: The problem states that 35% of the books are intended for children. Therefore, the number of books intended for children can be represented as 35% of the total number of books.
Step 2: We know that the number of books intended for children is 104. Therefore, we can write the equation: 35% of total number of bo... | 160 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Patricia is making a highlight film about her basketball team. She recorded video of every player and plans to put it all together in a longer movie. She has 130 seconds of the point guard,... | Step 1: Calculate the total time
Total time = 130 + 145 + 85 + 60 + 180 = 590 seconds
Step 2: Calculate the total number of players
Total players = 5
Step 3: Calculate the average time per player
Average time per player = Total time / Total players = 590 / 5 = 118 seconds
Step 4: Convert the average time per play... | Step 1: Calculate the total video time of all players by adding the time for each player.
Step 2: Divide the total video time of all players by the total number of players (5) to get the average time per player.
Step 3: Divide the total video time of the point guard (130 seconds) by the average time per player (14.2 se... | 2 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: James buys 20 coins of a cryptocurrency at $15 each. The value of the coins increases by 2/3. He sells coins to recoup his original investment. How many coins did he sell?
Answer:
| Step 1. First, let's determine the original value of the coins. James buys 20 coins of a cryptocurrency at $15 each. He recovers his original investment of $300 by selling coins at a 2/3 increase. So, we need to determine the value of the coins at the 2/3 increase. We start by finding the 2/3 increase in the value... | Step 1: Find the value of one coin before the increase in value.
Step 2: Find the value of one coin after the increase in value.
Step 3: Calculate the number of coins sold to recoup the original investment.
Step 4: Output the final answer on its own line as: '#### <answer>'
Step 1: Value of one coin after increase... | 12 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: In the park, the first rose bush has 12 red flowers. The second rose bush has 18 pink flowers. The third rose bush has 20 yellow flowers. The fourth rose bush has 8 orange flowers. For ... | Step 1: The first rose bush has 12 red flowers. The second rose bush has 18 pink flowers. The third rose bush has 20 yellow flowers. The fourth rose bush has 8 orange flowers.
Step 2: Lorelei picks 50% of the red roses, 50% pink roses, 25% of the yellow roses, and 25% orange roses.
Step 3: 50% of the red roses is 0.5 x... | Step 1: First, we need to find 50% of each type of rose. This is equal to half of the number. So, for the first rose bush, we have 12 x 0.5 = 6. For the second rose bush, we have 18 x 0.5 = 9. For the third rose bush, we have 20 x 0.5 = 10. For the fourth rose bush, we have 8 x 0.5 = 4.
Step 2: Then, we need to ... | 22 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Leo's assignment was divided into three parts. He finished the first part of his assignment in 25 minutes. It took him twice as long to finish the second part. If he was able to finish his ... | Step 1: Leo finished the first part in 25 minutes. He finished the second part in twice as long as the first part, which is 25 * 2 = 50 minutes. Therefore, the third part took 50 minutes to finish.
Step 2: Leo finished the assignment in 2 hours, which is 120 minutes. Since we already know that the first two parts took ... | Step 1: Find out how long it took Leo to finish the second part of the assignment.
Step 2: Find the time it took Leo to finish the first part of the assignment.
Step 3: Find the time it took Leo to finish the third part of the assignment.
Step 4: Use the time for the first part and the second part to calculate the tim... | 45 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Susie has 572 beans in the jar. One-fourth of them are red and one-third of the remaining beans are white. Then half of the remaining are green beans. How many green beans are there?
Answe... | Step 1: Calculate the total number of red beans.
One-fourth of 572 is 572 / 4 = 143
Step 2: Calculate the number of beans that are not red.
572 - 143 = 429
Step 3: Calculate the total number of beans that are white.
One-third of 429 is 429 / 3 = 143
Step 4: Calculate the number of beans that are not red or white.
42... | Step 1: First, calculate the number of beans that are red.
Step 2: Then, calculate the number of beans that are white.
Step 3: Next, find the number of beans that are green.
Step 4: Calculate the total number of beans that are green.
#### 570
Explanation:
Step 1: First, calculate the number of beans that are red.... | 143 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Jim collects model cars, and he has 301 models total. Jim has 4 times as many Buicks as Fords, and 3 more than twice the number of Fords than Chevys. How many Buicks does Jim have?
Answe... | Step 1: Define the variables
Let F = number of Fords, B = number of Buicks, and C = number of Chevys.
Step 2: Write equations
Since Jim has 4 times as many Buicks as Fords, B = 4F.
Since Jim has 3 more than twice the number of Fords than Chevys, F = 2C + 3.
Since Jim has a total of 301 models, B + F + C = 301.
Step 3... | Step 1: Let's denote the number of Fords as x.
Step 2: Since Jim has 3 more than twice the number of Fords than Chevys, the number of Chevys can be denoted as y. Therefore, the number of Fords is 2y + 3.
Step 3: Since Jim has 4 times as many Buicks as Fords, the number of Buicks can be denoted as 4(2y + 3).
Step 4:... | 220 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Peter has a plan to take his family on a vacation to Germany. He needs $5,000 to cover all the spending for the travel, and he has $2,900 in savings right now. If he can save up $700 each m... | Step 1: Calculate the amount of money Peter still needs to save to reach his goal.
Step 2: Determine the number of months Peter needs to wait to reach his goal.
Step 3: Calculate the total number of months.
Step 4: Output the final answer.
Step 5: Step 4: Calculate the amount of money Peter still needs to save to ... | Step 1: Determine the total amount of money Peter needs to save.
Step 2: Determine how much money Peter has to save each month.
Step 3: Calculate how many months it will take Peter to save the total amount of money needed.
Step 4: Output the final answer.
Step 1:
The total amount of money Peter needs to save is $5,000... | 3 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Last year, Peter organized a Fun Run for his community project and 200 people signed up. Forty people did not show up to run. This year, there will be twice as many runners as last year. Ho... | Step 1: Calculate the number of runners this year without considering the people who didn't show up.
200 (last year's participants) - 40 (didn't show up) = 160
Step 2: Calculate the number of runners this year when there are twice as many participants as last year.
160 * 2 = 320
Step 3: Print the final answer on its ow... | Step 1: Let the number of runners this year be x.
Step 2: Since there will be twice as many runners as last year, the number of runners this year will be 2x.
Step 3: Since 40 people did not show up last year, the number of runners last year was 200 - 40 = 160.
Step 4: Since the number of runners this year is twice ... | 320 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Dulce's father has eight orange trees on his farm. If each tree has 200 fruits and Dulce picks 2/5 of the oranges from each tree, calculate the total number of fruits remaining in all the t... | Step 1: Calculate the total number of fruits picked from all the trees. Dulce picks 2/5 of 200 fruits from each tree. So, the number of fruits picked from each tree is 2/5 * 200 = 80. So, the total number of fruits picked from all the trees is 80 * 8 = 640.
Step 2: Calculate the total number of fruits remaining in all ... | Step 1: First, let's calculate the total number of fruits in all the trees.
8 trees * 200 fruits per tree = 1600 fruits
Step 2: Now, let's calculate the number of fruits Dulce picks from each tree.
2/5 * 200 fruits per tree = 80 fruits per tree
Step 3: Finally, let's calculate the total number of fruits remaining in ... | 960 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Padma is trading cards with Robert. Padma started with 75 cards and traded 2 or her valuable ones for 10 of Robert's cards. Robert started with 88 of his own cards and traded another 8 of h... | Step 1: Padma started with 75 cards and traded 2 for 10 of Robert's cards.
Padma's cards after trading: 75 - 2 = 73 cards
Step 2: Padma traded 2 cards for 10 of Robert's cards.
Padma traded a total of 2 + 10 = 12 cards.
Step 3: Robert started with 88 cards and traded 8 of his cards for 15 of Padma's cards.
R... | Step 1: Identify what we know.
- Padma starts with 75 cards.
- Padma trades 2 cards for 10 cards.
- Robert starts with 88 cards.
- Robert trades 8 cards for 15 cards.
Step 2: Calculate the total cards traded by Padma.
- Padma trades 2 cards for 10 cards.
- To find out how many cards Padma traded in total, we divide 2 b... | 35 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: There are 920 deer in a park. 10% of the deer have 8 antlers, and a quarter of that number also have albino fur. How many albino 8-antlered deer are there?
Answer:
| Step 1: Calculate the number of deer with 8 antlers.
10% of 920 deer = 0.1 × 920 = 92 deer with 8 antlers.
Step 2: Calculate the number of deer with 8 antlers and albino fur.
A quarter of 92 deer = 0.25 × 92 = 23 deer with 8 antlers and albino fur.
Step 3: Calculate the number of albino 8-antlered deer.
Number of albin... | Step 1: First, let's find the total number of deer that have 8 antlers.
Since 10% of the deer have 8 antlers, the number of deer with 8 antlers is 10% of 920, which is: 0.1 * 920 = 92.
Step 2: Next, let's find the number of deer that also have albino fur. Since a quarter of the deer with 8 antlers also have albino fu... | 23 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Allison went to the craft store with her friend Marie to buy some glue sticks and construction paper. Allison bought 8 more glue sticks than Marie, but Marie bought six times as many packs ... | Step 1: Allison bought 8 more glue sticks than Marie.
Step 2: Marie bought 30 packs of construction paper, which is 6 times as many packs as Allison bought.
Step 3: Allison bought 30 / 6 = 5 packs of construction paper, so Allison bought 5 packs of construction paper.
Step 4: Allison bought 8 more glue sticks than Mari... | Step 1: Let the number of glue sticks bought by Marie be G and the number of packs of construction paper bought by Allison be C.
Step 2: From the information given, we know that G = 6C, since Marie bought six times as many packs of construction paper as Allison.
Step 3: We also know that C + G = 15, since Marie boug... | 28 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: James gets bored with his game so decides to play a different one. That game promises 100 hours of gameplay but 80% of that is boring grinding. However, the expansion does add another 30 ... | Step 1: Calculate the number of hours of gameplay in the main game. 100 x 0.8 = 80 hours.
Step 2: Calculate the number of hours of enjoyable gameplay in the expansion. 100 + 30 = 130 hours.
Step 3: Subtract the number of boring grinding hours from the total hours of gameplay in the expansion. 130 - 80 = 50 hours.
####... | Step 1: Convert the hours promised by the game to hours James actually gets to enjoy.
Step 2: Calculate the enjoyable gameplay by subtracting the hours of boring grinding from the hours James gets to enjoy.
#### 26
Explanation:
Step 1: 100 hours promised - 80% boredom = 100 - 0.8 * 100 = 100 - 80 = 20 hours enjoyable.... | 50 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Jane is trying to decide whether to buy a house or a trailer. A house costs $480,000 and a trailer costs $120,000. Each loan will be paid in monthly installments over 20 years. How much mor... | Step 1: Determine the total number of payments. The loan will be paid for 20 years and there will be 12 payments per year. Since there are 20 years, there will be 20 x 12 = 240 payments in total.
Step 2: Calculate the monthly payment for the house. To calculate the monthly payment, divide the total cost of the house ... | Step 1: Determine the monthly payment for the house.
The monthly payment for the house will be equal to the annual payment divided by 12.
\frac{480,000}{12}=40,000
Step 2: Determine the monthly payment for the trailer.
The monthly payment for the trailer will be equal to the annual payment divided by 12.
\frac{120,000... | 1500 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Mia is buying Christmas gifts for her family. She has spent $30 on each of her 3 siblings, and the rest of her spending was for her parents. If Mia spent a total of $150 on Christmas gifts ... | Step 1: Let's denote the value of each parent’s gift as P.
Step 2: Mia spent $30 on each of her 3 siblings, so the total amount she spent on her siblings is 3 x 30 = 90 dollars.
Step 3: The total amount Mia spent on her parents is the remainder of the total amount she spent on gifts, which is 150 - 90 = 60 dollars.
... | Step 1: Let's define variables.
M = amount spent on Mia's siblings
P = amount spent on each parent
Step 2: Mia has spent $30 on each of her 3 siblings, so the amount spent on her siblings is 3*M. The remaining money is spent on her parents. The amount spent on her parents is 150-M.
Step 3: Now, we can set up a... | 30 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Clare's mother gave her $47 to go to the store. Clare bought 4 loaves of bread and 2 cartons of milk. Each loaf of bread cost $2 and each carton of milk cost $2. How much money does Clare h... | Step 1: Calculate the total cost of bread. 4 loaves of bread * $2 per loaf = $8
Step 2: Calculate the total cost of milk. 2 cartons of milk * $2 per carton = $4
Step 3: Calculate the total cost of all the items. $8 (bread) + $4 (milk) = $12
Step 4: Calculate how much money Clare has left. $47 (initial amount) - $12 (to... | Step 1: Let's denote the amount of money Clare had at the beginning as x.
Step 2: Clare spent money on 4 loaves of bread and 2 cartons of milk. This means she spent a total of 4x + 2y dollars.
Step 3: Since the problem states that the amount of money Clare had at the beginning is $47, we can write the following equa... | 35 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Oshea bought 200 basil seeds. He wants to plant them in planters. He has 4 large planters that can hold 20 seeds each. He also has small planters that can hold 4 seeds each. How many small ... | Step 1: Calculate the number of seeds that can be planted in the large planters. 4 large planters × 20 seeds per planter = 80 seeds.
Step 2: Calculate the number of seeds that can be planted in the small planters. 200 seeds – 80 seeds = 120 seeds.
Step 3: Calculate the number of small planters needed. 120 seeds ÷ 4 see... | Step 1: Determine the number of seeds that can be held in the large planters. 4 planters * 20 seeds per planter = 80 seeds.
Step 2: Determine how many seeds are left after planting in the large planters. 200 seeds - 80 seeds = 120 seeds left.
Step 3: Determine the number of seeds that can be held in one small planter. ... | 30 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Eric sorted 150 colored pencils into 5 containers for his art class. Before class, another teacher brought him 30 more pencils. How many can he evenly distribute between the five containers... | Step 1:
Eric had 5 containers of pencils initially.
Step 2:
He now has a total of 150 + 30 = 180 pencils.
Step 3:
The number of pencils each container can now be evenly distributed by dividing the total number of pencils (180) by the number of containers (5).
Step 4:
180 / 5 = 36
So, Eric can evenly distrib... | Step 1. Subtract the initial number of pencils from the total.
150 - 30 = 120
Step 2. Divide the result by the number of containers.
120 ÷ 5 = 24
Step 3. The answer is 24.#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
#### 24
##... | 36 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Oleg is an event organizer. He is organizing an event with 80 guests where 40 of them are men, half the number of men are women, and the rest are children. If he added 10 children to the gu... | Step 1: Determine the number of women.
Since there are 40 men and women are half the number of men, the number of women is 40 / 2 = 20.
Step 2: Determine the initial number of children.
Number of guests = 80, Number of men = 40, Number of women = 20, so the number of children is 80 - (40 + 20) = 20.
Step 3: Calculate... | Step 1: We need to determine the initial number of children at the event.
Step 2: Since 40 of the guests are men, the number of women is equal to the number of men, which is 40.
Step 3: We are given that the number of women is half the number of men, so the number of women is 40 / 2 = 20.
Step 4: Adding 10 children... | 30 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Stella collects stamps. She counted 50 pages in her collector's album. There are 5 rows of 30 stamps in each of the first 10 pages of her album. The rest of the pages each have 50 stamps. H... | Step 1: Identify the number of stamps in each row
There are 5 rows of 30 stamps, so each row has 5 x 30 = 150 stamps.
Step 2: Calculate the number of stamps in the first 10 pages
There are 10 pages with 150 stamps each, so there are 10 x 150 = 1500 stamps in the first 10 pages.
Step 3: Calculate the total number of s... | Step 1: Count the number of stamps on the first 10 pages.
In the first 10 pages, there are 5 rows with 30 stamps each. Therefore, there are 5 * 30 = 150 stamps in the first 10 pages.
Step 2: Count the number of stamps on the remaining pages.
Since there are 50 pages in total, the number of remaining pages is 50 - 10 = ... | 3500 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: A desert garden’s sprinkler system runs twice a day during the cool morning and evening hours. It waters the garden with four liters of water in the morning and six liters in the evening. H... | Step 1: Let the number of days the system runs be n.
Step 2: The total amount of water used in n days is 4n + 6n = 10n.
Step 3: The system uses 50 liters of water.
Step 4: The number of days it takes the system to use 50 liters of water is 50/10 = 5.
Step 5: The system takes 5 days to use 50 liters of water.
#### 5
No... | Step 1: Let \(x\) be the number of days that the sprinkler system waters the garden. We know that during the cool morning and evening hours, the garden is watered twice a day.
Step 2: The total amount of water used by the sprinkler system per day is 4 + 6 = 10 liters.
Step 3: The total amount of water used by the sp... | 5 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Mr. Langsley commutes to work every day by bus. The bus picks him up at 6:00 a.m. and takes forty minutes to arrive at the first station. If Mr. Langsley arrives at work at 9:00 a.m., what'... | Step 1: Mr. Langsley arrives at work at 9:00 a.m. He was picked up at 6:00 a.m. and it took forty minutes to arrive at the first station.
Step 2: To find the total time taken for the journey, we need to subtract the time taken for Mr. Langsley to arrive at the first station from the time he is picked up.
Step 3: Fir... | Step 1: First, let's determine how many buses Mr. Langsley takes to get to work. We know that the bus arrives at 6:00 a.m. and takes 40 minutes to get to the first station. To find the number of buses, we need to divide the time taken to get to the first station by the time taken to get to the next station, which is 40... | 140 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Janessa has a plan to give her brother Dexter his first collection of baseball cards. She currently has 4 cards in addition to the 13 that her father gave her. She ordered a collection of ... | Step 1: To solve this problem, we need to start by identifying the number of cards that Janessa initially had and the number of cards she received as gifts.
Step 2: Janessa initially had 4 cards and received 13 cards from her father, making a total of 4 + 13 = 17 cards.
Step 3: Next, we need to add the 36 cards she ... | Step 1: Determine the total number of cards Janessa initially had.
Janessa currently has 4 cards and 13 cards from her father, so she initially had 4 + 13 = 17 cards.
Step 2: Calculate the number of cards Janessa has after giving Dexter some of his cards.
Janessa ordered 36 cards, but threw away 4, so she had 36 - 4 =... | 20 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Daryl is loading crates at a warehouse and wants to make sure that they are not overloaded. Each crate can weigh up to 20kg and he has 15 crates he can fill. He has 4 bags of nails to load,... | Step 1: Calculate the total weight of the crates that Daryl can fill.
Total weight = number of crates * weight per crate = 15 * 20 = 300kg.
Step 2: Calculate the total weight of the items Daryl is bringing to load.
Weight of nails = 4 * 5 = 20kg
Weight of hammers = 12 * 5 = 60kg
Weight of wooden planks = 10 * 30 = 300... | Step 1: Calculate the maximum weight that can be loaded per crate.
Maximum weight per crate = 20 kg.
Step 2: Calculate the total weight of the items that Daryl has.
Weight of nails = 4 x 5 = 20kg
Weight of hammers = 12 x 5 = 60kg
Weight of wooden planks = 10 x 30 = 300kg
Total weight = 20 + 60 + 300 = 380kg
Step 3: C... | 80 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Kwame studied for the history test for 2.5 hours. Connor studied for 1.5 hours and Lexia studied for 97 minutes. How many minutes more did Kwame and Connor study than Lexia?
Answer:
| Step 1: Convert all studying times to minutes.
Kwame studied for 2.5 hours * 60 minutes/hour = 150 minutes.
Connor studied for 1.5 hours * 60 minutes/hour = 90 minutes.
Step 2: Subtract the total studying time of Kwame and Connor from Lexia's studying time.
Step 3: Convert the total minutes to a common unit (minutes) f... | Step 1: Convert the study time of Kwame to minutes, 2.5 hours * 60 minutes/hour = 150 minutes
Step 2: Convert the study time of Connor to minutes, 1.5 hours * 60 minutes/hour = 90 minutes
Step 3: Convert the study time of Lexia to minutes, 97 minutes
Step 4: Calculate the total study time of Kwame and Connor, 150 minut... | 143 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Aunt May milks her cows twice a day. This morning she got 365 gallons of milk. This evening she got 380 gallons. She sold 612 gallons to the local ice cream factory. She had 15 gallons lef... | Step 1: Add the milk collected this morning and this evening
365 + 380 = 745
Step 2: Subtract the milk that was sold
745 - 612 = 133
Step 3: Add the leftover milk from yesterday
133 + 15 = 148
#### 148 | Step 1: Let's start by defining a variable to represent the number of gallons Aunt May had on the previous day, which we'll call x.
Step 2: The total number of gallons of milk Aunt May has is the sum of the gallons she got this morning, this evening, and the gallons she had left over from yesterday.
Step 3: This c... | 148 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Mehki is 10 years older than Jordyn. Jordyn's age is double Zrinka's age. If Zrinka is 6 years old, how many years old is Mehki?
Answer:
| Step 1: Determine Zrinka's age
Zrinka's age = 6 years
Step 2: Determine Jordyn's age
Jordyn's age = 2 * Zrinka's age = 2 * 6 = 12 years
Step 3: Determine Mehki's age
Mehki's age = Jordyn's age + 10 years = 12 + 10 = 22 years
#### 22 | Step 1: Let Zrinka's age be X. Then Jordyn's age is 2X. Mehki's age is 10 years more than Jordyn's age, which is 2X + 10.
Step 2: Given that Zrinka is 6 years old, X = 6.
Step 3: Mehki's age is 2X + 10 and X = 6, therefore Mehki's age is 2(6) + 10 = 28.
#### 28 | 22 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: A single train car can carry 60 passengers. A 747 airplane can carry 366 passengers. How many more passengers can a train with 16 cars carry than 2 airplanes?
Answer:
| Step 1: Calculate the number of passengers the train can carry
16 cars x 60 passengers per car = 960 passengers
Step 2: Calculate the number of passengers 2 airplanes can carry
2 x 366 passengers per airplane = 732 passengers
Step 3: Find the difference between the two amounts
960 - 732 = 228
#### 228 | Step 1: First, let's determine how many passengers the 2 airplanes can carry.
Step 2: Since a single train car can carry 60 passengers, a 2-airplane train can carry 60 * 2 = 120 passengers.
Step 3: Now, let's determine how many passengers a train with 16 cars can carry.
Step 4: Since a single train car can carry 60 pas... | 228 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: The tallest of 3 trees is 108 feet. The middle sized tree is 6 feet less than half the height of the tallest tree. The smallest tree is 1/4 the height of the middle tree. How tall is the ... | Step 1: The tallest tree is 108 feet. Let T = the height of the tallest tree. The middle tree is 6 feet less than half the height of the tallest tree. Let M = the height of the middle tree. Therefore, M = T/2 - 6
Step 2: The middle-sized tree is 1/4 the height of the middle tree. Therefore, the smallest tree is 1/... | Step 1: To find the height of the middle-sized tree, let's call the height of the tallest tree x. Since the middle-sized tree is 6 feet less than half the height of the tallest tree, we can express the height of the middle tree as (x/2) - 6.
Step 2: The height of the smallest tree is 1/4 of the height of the middle ... | 12 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Carla, Kyle, and Tasha caught 36 fish. If Kyle and Tasha caught the same number of fish and Carla caught 8, how many fish did Kyle catch?
Answer:
| Step 1: Let's use the variable x to represent the number of fish Kyle caught. Since Kyle and Tasha caught the same number of fish, the number of fish Tasha caught is also x.
Step 2: Carla caught 8 fish, so the total number of fish is the sum of the number of fish Carla caught, Kyle caught, and Tasha caught: 8 + x + x... | Step 1: Let's use a variable, such as 'x', to represent the number of fish that Kyle caught.
Step 2: Since Carla caught 8 fish, Kyle and Tasha each caught x-8 fish.
Step 3: Since Kyle and Tasha caught the same number of fish, we can set up the equation x-8 = x-8.
Step 4: To solve for x, we can add 8 to both sides o... | 14 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: A store received 20 pallets of paper products to stock. Half the pallets were paper towels, a quarter were tissues, and a fifth were paper plates. The rest were paper cups. How many pallets... | Step 1. Let x represent the number of pallets of paper cups received. The store received 20 pallets in total.
Step 2. Half the pallets were paper towels, so the number of paper towels is 20/2 = 10.
Step 3. A quarter of the pallets were tissues, so the number of tissues is 20/4 = 5.
Step 4. A fifth of the pallets... | Step 1: Calculate the total number of paper products received.
20 (paper towels) + 5 (tissues) + 4 (paper plates) = 29
Step 2: Calculate the number of pallets of paper products received.
20 (total pallets) - 29 (paper products) = -9
Step 3: The negative number indicates a mistake in the problem. The correct approach ... | 1 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Miss Davis gave 15 popsicle sticks to each of the 10 groups in her class. How many sticks does she have left if she had 170 popsicle sticks?
Answer:
| Step 1: Calculate the total number of popsicle sticks given out.
15 sticks per group * 10 groups = 150 sticks
Step 2: Subtract the number of sticks given out from the original number of sticks.
170 sticks - 150 sticks = 20 sticks
#### 20 | Step 1: Let's define the number of sticks given to each group as x. Therefore, the total number of sticks given is 10x.
Step 2: The total number of sticks Miss Davis had is 170. Therefore, we can set up the equation 10x + 15 = 170.
Step 3: To solve for x, we need to isolate the variable. We can do this by subtracti... | 20 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Mark is reading books, for 2 hours each day. He decided to increase his time spent on reading books weekly, by 4 hours. How much time does Mark want to spend during one week on reading book... | Step 1: Convert the 2 hours per day to hours per week, since Mark is increasing his weekly time.
2 hours * 7 days = 14 hours.
Step 2: Convert the 4 hours per week increase to hours per week.
4 hours * 1 week = 4 hours.
Step 3: Calculate Mark's total desired time per week.
14 hours + 4 hours = 18 hours.
#### 18 | Step 1: Define variables and understand the problem.
Let W be the amount of time Mark wants to spend on reading books in one week. Step 2: Express the initial and final time spent on reading books each day in terms of W. Step 3: Multiply the number of days in a week by the initial time spent on reading books each day t... | 18 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Ali had a collection of seashells. He started with 180 seashells. He then gave away 40 seashells to his friends. He also gave 30 seashells to his brothers. If he sold half of the remaining ... | Step 1: Calculate how many seashells Ali had after giving away 40 to his friends.
180 - 40 = 140
Step 2: Calculate how many seashells Ali had after giving 30 to his brothers.
140 - 30 = 110
Step 3: Calculate half of the remaining seashells.
110 / 2 = 55
Ali had 55 seashells left.
#### 55 | Step 1: Calculate how many seashells Ali had left after giving some away to his friends and his brothers.
Step 2: Determine how many seashells Ali had left after selling half of the remaining seashells.
Step 3: Output the final answer as requested.
## Step 1: Calculate how many seashells Ali had left after giving some... | 55 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: James buys 6 t-shirts for 50% off. They each cost $20. How much did he pay?
Answer:
| Step 1: Calculate the discount per t-shirt. 50% off means 50% of the original price, which is 0.5 * $20 = $10 off per t-shirt.
Step 2: Determine the price per t-shirt after the discount. Since he buys 6 t-shirts for $10 off each, the price per t-shirt will be 20 - 10 = $10 per t-shirt.
Step 3: Calculate the total amo... | Step 1: First, we need to find out how much each shirt costs before the 50% discount.
Let's call the original price of one shirt 'x'.
Then, x - 50% of x = 20
0.5x = 20
x = 40
Step 2: Since James buys 6 shirts, we multiply the original price of one shirt by 6:
6 x 40 = 240
Step 3: We need to find out... | 60 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Alicia has to buy some books for the new school year. She buys 2 math books, 3 art books, and 6 science books, for a total of $30. If both the math and science books cost $3 each, what was ... | Step 1: Let the cost of each art book be x.
Step 2: Since Alicia buys 2 math books and 3 art books and 6 science books for $30, we can write the following equation: 2(3) + 3x + 6(3) = 30
Step 3: Simplify the equation: 6 + 3x + 18 = 30
Step 4: Combine like terms: 24 + 3x = 30
Step 5: Subtract 24 from both sides: 3x = 6
... | Step 1: Let's denote the cost of each art book by 'x'.
Step 2: We can write an equation to represent the situation, based on the given information. The total cost of the books is $30. The cost of 2 math books is $3 * 2 = $6. The cost of 3 art books is $3 * 3 = $9. The cost of 6 science books is $3 * 6 = $18. Therefor... | 2 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: A jar contains 9 blue pens, 21 black pens, and 6 red pens. Four blue pens are removed and then seven black pens are removed. How many pens are left in the jar?
Answer:
| Step 1: Count the total number of pens initially in the jar: 9 blue pens + 21 black pens + 6 red pens = 36 pens.
Step 2: Subtract the number of blue pens removed from the total: 36 - 4 = 32 pens left.
Step 3: Subtract the number of black pens removed from the remaining number of pens: 32 - 7 = 25 pens left.
#### 25 | Step 1: Calculate the total number of pens in the jar initially.
9 blue pens + 21 black pens + 6 red pens = 36 pens.
Step 2: Determine how many pens are left after removing 4 blue pens.
9 blue pens - 4 = 5 blue pens.
5 blue pens + 21 black pens + 6 red pens = 36 pens.
Step 3: Determine how many pens are lef... | 25 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Three siblings are born 5 years apart, each. If the eldest child is 20 years old now, what's the total of the ages of the three siblings 10 years from now?
Answer:
| Step 1: The first child is 20 years old now, so the second child is 20 - 5 = 15 years old, and the third child is 20 - 5 - 5 = 10 years old.
Step 2: Ten years from now, the eldest child will be 20 + 10 = 30 years old, the second child will be 15 + 10 = 25 years old, and the third child will be 10 + 10 = 20 years old.
S... | Step 1: Let the ages of the three siblings now be x, y, z.
Step 2: Since they are born 5 years apart, we have the following equations: y = x + 5 and z = x + 10.
Step 3: So, x = 20
Step 4: We can now calculate the ages of the three siblings 10 years from now: x+5=25, y+5=25+5=30, z+10=30+10=40
Step 5: The total of... | 75 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Mike watches TV for 4 hours every day. On the days he plays video games he plays for half as long as he watches TV. If he plays video games 3 days a week how long does he spend watching T... | Step 1: Find the total time Mike watches TV in a week.
Mike watches TV for 4 hours every day for 7 days. The total time Mike watches TV is 4 * 7 = 28 hours.
Step 2: Find the total time Mike plays video games in a week.
On the days he plays video games he plays for half as long as he watches TV. Therefore, he plays for... | Step 1: Define the variables and the question.
Let T be the time spent watching TV and G be the time spent playing video games.
Step 2: Create a system of equations.
T + G = 4, 0.5T + 1.5G = 3.
Step 3: Solve the system of equations by elimination or substitution.
To eliminate one of the variables, multiply the first ... | 34 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Michael saved 5 of his cookies to give Sarah, who saved a third of her 9 cupcakes to give to Michael. How many desserts does Sarah end up with?
Answer:
| Step 1: First, find out how many cupcakes Sarah saved. She saved 1/3 of 9 cupcakes, which is 9 x 1/3 = 3 cupcakes. Since she had 9 cupcakes initially, she had 9 - 3 = 6 cupcakes.
Step 2: Then, find out how many desserts Michael gives to Sarah. He saved 5 cookies for Sarah.
Step 3: Find out how many desserts Sarah ends ... | Step 1: First, find out how many desserts Sarah gave to Michael.
Step 2: Michael saved 5 of his cookies.
Step 3: Sarah gave 1/3 of her 9 cupcakes to Michael.
Step 4: To find the number of desserts Sarah gave to Michael, multiply 9 by 1/3.
9 * 1/3 = 3 desserts
Step 5: Now find out how many desserts Sarah has left.
... | 11 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Katie has 13 pink marbles. She has 9 fewer orange marbles than pink marbles. She has 4 times as many purple marbles as orange marbles. How many marbles does Katie have in all?
Answer:
| Step 1: Katie has 13 pink marbles.
Step 2: She has 9 fewer orange marbles than pink marbles, so she has 13 - 9 = 4 orange marbles.
Step 3: She has 4 times as many purple marbles as orange marbles. 4 * 4 = 16 purple marbles.
Step 4: 13 + 4 + 16 = 33 marbles in all.
#### 33 | Step 1: Let's say there are x orange marbles.
Step 2: Since there are 9 fewer orange marbles than pink marbles, there are 13 - x pink marbles.
Step 3: Since there are 4 times as many purple marbles as orange marbles, there are 4x purple marbles.
Step 4: The total number of marbles is the sum of pink, orange, and purple... | 33 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Erin runs her own launderette and needs to cash in the change from the machines. There are 80 quarters and 100 dimes in every machine in the launderette. When Erin empties all of the machin... | Step 1: Let $x$ represent the number of machines in the launderette. Erin has $80x$ quarters and $100x$ dimes.
Step 2: Since each quarter is worth 25 cents or $\frac{1}{4}$ dollars and each dime is worth 10 cents or $\frac{1}{10}$ dollars, the total amount of money Erin receives from the machines is given by the equa... | Step 1: First, we must convert the amounts of money from the quarters and dimes into cents so that we can add them together. Since 1 quarter is worth 25 cents, 80 quarters are worth $2,000 (80 * 25 cents) and 100 dimes are worth $10 (100 * 10 cents).
Step 2: Next, we can add the values of the quarters and dimes toget... | 3 |
You are a careful reasoner. Solve step-by-step. At the end, output the final answer on its own line as: '#### <answer>'
Question: Richard can clean his room in 22 minutes. Cory takes 3 minutes more than Richard to clean her room while Blake can clean his room 4 minutes more quickly than Cory. If they have to clean the... | Richard = 22 min
Cory = 22 + 3 = 25 min
Blake = 25 – 4 = 21 min
Total time for Richard, Cory, and Blake = (2 x 22) + (2 x 25) + (2 x 21) = 44 + 50 + 42 = 136 min
#### 136 | Richard clean his room in 22 minutes. Cory takes 3 minutes more than Richard to clean her room. So Cory takes 22 + 3 = 25 minutes to clean her room. Blake takes 3 - 4 = 1 minute less than Cory to clean her room. So Blake takes 25 - 1 = 24 minutes to clean his room.
Richard cleans his room in 22 minutes. Cory takes 25 m... | 136 |
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