source stringclasses 28
values | source_dataset stringclasses 2
values | quality_metrics null | prompt stringlengths 1 2.76k | response stringlengths 1 148k | answer stringlengths 1 8.62k | int_answer stringclasses 868
values | input_ids listlengths 32 512 | attention_mask listlengths 32 512 | bucket_id int64 0 9 | answer_token int64 0 1k |
|---|---|---|---|---|---|---|---|---|---|---|
orca_math | AI-MO/NuminaMath-CoT | null | There were 27 boys and 35 girls on the playground at recess. There were _____ children on the playground at recess. | There were 62 children on the playground at recess. (27 boys + 35 girls = $\boxed{62}$ children) | 62 | 62 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Bianca earned 5 points for each bag of cans she recycled. If she had 17 bags, but didn't recycle 8 of them, how many points would she have earned? | Bianca recycled 17 - 8 = 9 bags of cans.
For each bag of cans, she earned 5 points, so for 9 bags, she would have earned 9 * 5 = $\boxed{45}$ points. | 45 | 45 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Jack received 6 emails in the morning and some emails in the afternoon. He received 2 more emails in the afternoon than in the morning. How many emails did Jack receive in the afternoon? | If Jack received 6 emails in the morning and he received 2 more emails in the afternoon than in the morning, then he received 6 + 2 = $\boxed{8}$ emails in the afternoon. | 8 | 8 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Leif’s apple tree has 14 apples and his orange tree has 2 dozen oranges. How many more oranges does he have than apples? | Leif has 14 apples.
His orange tree has 2 dozen oranges. 1 dozen is equal to 12, so 2 dozen is 2 x 12 = 24 oranges.
To find out how many more oranges he has than apples, we subtract the number of apples from the number of oranges:
24 oranges - 14 apples = $\boxed{10}$ more oranges than apples. | 10 | 10 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Find the value of adding 3 to the number of diagonals in the rectangle. | A rectangle has 2 diagonals. If we add 3 to the number of diagonals in the rectangle, we get:
2 (number of diagonals in a rectangle) + 3 = 5.
So the value is $\boxed{5}$ . | 5 | 5 | [
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orca_math | AI-MO/NuminaMath-CoT | null | The zoo keeps 35 female (a) animals. Males outnumber females by 7. How many (a) animals are there in all? | If males outnumber females by 7, then there are 35 + 7 = 42 male (a) animals.
To find the total number of (a) animals, we add the number of females and males together:
35 females + 42 males = $\boxed{77}$ (a) animals in all. | 77 | 77 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Jessica has 3 dozen red marbles. Sandy has 4 times more red marbles than Jessica. How many red marbles does Sandy have? | If Jessica has 3 dozen red marbles, that means she has 3 x 12 = 36 red marbles.
Sandy has 4 times more red marbles than Jessica, so Sandy has 4 x 36 = $\boxed{144}$ red marbles. | 144 | 144 | [
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orca_math | AI-MO/NuminaMath-CoT | null | The Sumata family took a vacation by car. Each day they drove 250 miles. They drove 1250 miles in total. How many days did their vacation last? | To find out how many days their vacation lasted, we need to divide the total miles driven by the number of miles they drove each day.
Total miles driven = 1250 miles
Miles driven each day = 250 miles
Number of days = Total miles driven / Miles driven each day
Number of days = 1250 miles / 250 miles per day
Number of ... | 5 | 5 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Eugene has 51.0 pencils. He gives some pencils to Joyce and has 45 pencils left. How many pencils did Eugene give to Joyce? | Eugene had 51.0 pencils initially and was left with 45 pencils after giving some to Joyce. To find out how many pencils he gave to Joyce, we subtract the number of pencils he has left from the initial number of pencils he had:
51.0 pencils (initial) - 45 pencils (left) = 6 pencils (given to Joyce)
Eugene gave Joyce $... | 6 | 6 | [
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orca_math | AI-MO/NuminaMath-CoT | null | 2 birds and 6 storks were sitting on the fence. 3 more birds came to join them. How many more storks than birds are sitting on the fence? | Initially, there were 2 birds and 6 storks on the fence. Then 3 more birds came to join them, making the total number of birds 2 + 3 = 5 birds.
Now, to find out how many more storks than birds are sitting on the fence, we subtract the number of birds from the number of storks:
6 storks - 5 birds = $\boxed{1}$ more s... | 1 | 1 | [
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orca_math | AI-MO/NuminaMath-CoT | null | For Halloween, Sarah received 66 pieces of candy from neighbors and 15 pieces from her older sister. She ate a certain number of pieces a day, and the candy lasted her 9 days. How many pieces of candy did she eat per day? | To find out how many pieces of candy Sarah ate per day, we first need to determine the total number of pieces of candy she had.
She received 66 pieces from neighbors and 15 pieces from her sister, so the total is:
66 + 15 = 81 pieces of candy
The candy lasted her 9 days, so to find out how many pieces she ate per d... | 9 | 9 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Tom had 27 pennies and 15 dimes in his bank. His dad gave him 33 dimes and 49 nickels. How many dimes does he have now? | Tom originally had 15 dimes. His dad gave him 33 more dimes.
To find out how many dimes he has now, we add the two amounts together:
15 (original dimes) + 33 (dimes given by dad) = 48 dimes
Tom now has $\boxed{48}$ dimes. | 48 | 48 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Big boxes contain 7 dolls each. Small boxes contain 4 dolls each. There are 5 big boxes and 9 small boxes. How many dolls are there in total? | To find the total number of dolls, we need to calculate the number of dolls in both the big boxes and the small boxes and then add them together.
For the big boxes:
5 big boxes * 7 dolls per big box = 35 dolls
For the small boxes:
9 small boxes * 4 dolls per small box = 36 dolls
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orca_math | AI-MO/NuminaMath-CoT | null | There are 10 balls. Jungkook wants to put 5 balls in one box. How many boxes does he need at this time? | Jungkook wants to put 5 balls in one box, so if he has 10 balls, he would need 10 / 5 = $\boxed{2}$ boxes to hold all the balls. | 2 | 2 | [
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orca_math | AI-MO/NuminaMath-CoT | null | In a 60-item exam, Liza got 90% of the items correctly. Her best friend, Rose, got 2 more correct answers than her. How many incorrect answers did Rose have? | If Liza got 90% of the items correctly in a 60-item exam, she got:
90% of 60 = 0.90 * 60 = 54 correct answers.
Rose got 2 more correct answers than Liza, so Rose got:
54 + 2 = 56 correct answers.
The total number of items in the exam is 60, so the number of incorrect answers Rose had is:
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orca_math | AI-MO/NuminaMath-CoT | null | Maria's birthday is in 22 days. Her friend Lilly wants to buy her flowers so she saves $2 each day until Maria's birthday. If a flower costs $4, how many flowers can Lilly buy? | Lilly saves $2 each day for 22 days. To find out the total amount she saves, we multiply the amount she saves each day by the number of days:
$2/day * 22 days = $44
Now, if each flower costs $4, we can find out how many flowers Lilly can buy by dividing the total amount she has saved by the cost of one flower:
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orca_math | AI-MO/NuminaMath-CoT | null | Scott has 7 pairs of shoes. Anthony has 3 times as many pairs of shoes as Scott, and Jim has 2 less pairs than Anthony. How many more pairs of shoes does Anthony have compared to Jim? | Anthony has 3 times as many pairs of shoes as Scott, so Anthony has 3 * 7 = 21 pairs of shoes.
Jim has 2 less pairs than Anthony, so Jim has 21 - 2 = 19 pairs of shoes.
Therefore, Anthony has 21 - 19 = $\boxed{2}$ more pairs of shoes compared to Jim. | 2 | 2 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Katie had 81 DS games and her friends had some games. Katie has 22 more games than her friends. How many DS games do her friends have? | Let's call the number of DS games Katie's friends have F. According to the information given, Katie has 22 more games than her friends. So we can write the following equation:
Katie's games = Friends' games + 22
We know Katie has 81 games, so we can substitute that into the equation:
81 = F + 22
Now, we can solve f... | 59 | 59 | [
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gsm8k | AI-MO/NuminaMath-CoT | null | John buys 3 reels of 100m fishing line. He cuts it into 10m sections. How many sections does he get? | John starts with 3 reels of 100m fishing line each. To find the total length of fishing line he has, we multiply the number of reels by the length of each reel:
\[3 \times 100 = 300 \, \text{m}\]
Next, to find out how many 10m sections he can get from the total length of fishing line, we divide the total length by th... | 30 | 30 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Jesse has 21 bananas. If he shares them among 3 friends, each friend would get _____ bananas . | If Jesse shares 21 bananas among 3 friends, each friend would get 21 ÷ 3 = $\boxed{7}$ bananas. | 7 | 7 | [
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orca_math | AI-MO/NuminaMath-CoT | null | When 632-AB1=41, what number should go in B? | To solve for B, we need to isolate B on one side of the equation. Let's first rewrite the equation without the dash:
632 - AB1 = 41
Now, let's move 632 to the right side of the equation by subtracting it from both sides:
-AB1 = 41 - 632
Now we have:
-AB1 = -591
Since we are looking for a single digit to replace B... | 9 | 9 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Anais has 30 more toys than Kamari. Kamari has 65 toys in his box. How many toys are there altogether? | If Kamari has 65 toys and Anais has 30 more toys than Kamari, then Anais has 65 + 30 = 95 toys.
To find out how many toys there are altogether, we add Kamari's toys and Anais's toys together: 65 (Kamari's toys) + 95 (Anais's toys) = $\boxed{160}$ toys altogether. | 160 | 160 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Sally had 27 Pokemon cards. Dan has some new Pokemon cards. Sally bought 20 Pokemon cards. Now, Sally has 6 more Pokemon cards than Dan has. How many Pokemon cards does Dan have? | Let's call the number of Pokemon cards Dan has D.
Sally originally had 27 Pokemon cards and then she bought 20 more. So now, Sally has:
27 + 20 = 47 Pokemon cards.
We are told that Sally has 6 more Pokemon cards than Dan. So we can write the equation:
47 = D + 6
Now, we can solve for D by subtracting 6 from both sid... | 41 | 41 | [
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synthetic_math | AI-MO/NuminaMath-CoT | null | If \( f(x) = 5 - 4x \) and \( g(x) = x^2 + 2 \), find \( f(g(2)) \). | First, we calculate \( g(2) \):
$$ g(2) = (2)^2 + 2 = 4 + 2 = 6. $$
Then, substitute \( g(2) \) into \( f(x) \):
$$ f(g(2)) = f(6) = 5 - 4(6) = 5 - 24 = -19. $$
Thus, the final result is \( \boxed{-19} \). | -19 | -19 | [
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orca_math | AI-MO/NuminaMath-CoT | null | At the presentation, students take turns giving presentations. Eunjung will be the 6th speaker from the back, and the seven students in front of Eunjung will make the presentation. How many students are giving presentations? | If Eunjung is the 6th speaker from the back, and there are 7 students in front of Eunjung who will make the presentation, then we can calculate the total number of students giving presentations by adding the number of students in front of Eunjung, Eunjung herself, and the students behind her (which is 5, since she is t... | 13 | 13 | [
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orca_math | AI-MO/NuminaMath-CoT | null | You have collected 7 crickets. How many more crickets do you need to collect to have a certain number of crickets if you need to collect 4 more? | If you need to collect 4 more crickets, then you will have 7 (the number you already have) + 4 (the number you need to collect) = $\boxed{11}$ crickets in total. | 11 | 11 | [
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gsm8k | AI-MO/NuminaMath-CoT | null | 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... | Let's break down the process of creating the care package step by step, following Ken's actions:
1. **Initial Jelly Beans:** Ken starts by adding jelly beans to the box until its weight reaches 2 pounds. So, the weight of the box at this point is:
\[
\text{Weight after jelly beans} = 2 \, \text{pounds}
\]
2.... | 16 | 16 | [
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orca_math | AI-MO/NuminaMath-CoT | null | It is 78 miles to Grandma's house. Mr. Welch drove 35 miles. He stopped to buy a pie for dessert. Then he drove 18 miles and stopped to put gas in the car. How many more miles until he reaches Grandma's house? | Mr. Welch has driven a total of 35 miles + 18 miles = 53 miles so far.
To find out how many more miles he has to drive to reach Grandma's house, we subtract the miles he has already driven from the total distance to Grandma's house.
78 miles (total distance) - 53 miles (distance already driven) = 25 miles remaining.
... | 25 | 25 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Dilan, Martha, Phillip, and Veronica went to the park together to have some fun. They all had a different number of marbles. At the end of the day, they redistributed the marbles so they each had 15 marbles. If Dilan had 14 marbles, Martha had 20 marbles, and Veronica had 7 marbles, how many marbles did Phillip have in... | To find out how many marbles Phillip had initially, we first need to determine the total number of marbles they had together after redistribution and then subtract the number of marbles Dilan, Martha, and Veronica had initially.
After redistribution, each of the four friends had 15 marbles, so the total number of marb... | 19 | 19 | [
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orca_math | AI-MO/NuminaMath-CoT | null | What is the least number that should be added to some number, so the sum of the number is completely divisible by 23? The answer is 4. What is the original number? | Let's call the original number \( x \). According to the problem, when we add 4 to \( x \), the result is completely divisible by 23. This can be written as:
\( x + 4 \equiv 0 \mod 23 \)
To find \( x \), we need to find a number that, when 4 is added to it, leaves no remainder after division by 23. Since 4 is the rem... | 19 | 19 | [
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orca_math | AI-MO/NuminaMath-CoT | null | How much is 80% of 45 greater than 4/5 of 25? | First, let's calculate 80% of 45:
80% of 45 = 0.80 * 45 = 36
Next, let's calculate 4/5 of 25:
4/5 of 25 = (4/5) * 25 = (4 * 25) / 5 = 100 / 5 = 20
Now, let's find out how much greater 80% of 45 is than 4/5 of 25:
36 (80% of 45) - 20 (4/5 of 25) = 16
So, 80% of 45 is $\boxed{16}$ greater than 4/5 of 25. | 16 | 16 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Danielle's apartment has 6 rooms. Heidi's apartment has 3 times as many rooms as Danielle's apartment. Grant's apartment has 1/9 as many rooms as Heidi's apartment. How many rooms does Grant's apartment have? | Heidi's apartment has 3 times as many rooms as Danielle's, so Heidi has 6 * 3 = 18 rooms.
Grant's apartment has 1/9 as many rooms as Heidi's, so Grant has 18 * (1/9) = $\boxed{2}$ rooms. | 2 | 2 | [
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orca_math | AI-MO/NuminaMath-CoT | null | A group of 5 friends went into a restaurant. The chef already had 20 chicken wings cooked but cooked 25 more for the group. If they each got the same amount, how many would each person get? | The chef had 20 chicken wings already cooked and cooked 25 more for the group. So, the total number of chicken wings is:
20 (already cooked) + 25 (cooked for the group) = 45 chicken wings
There are 5 friends in the group, and they each get the same amount of chicken wings. To find out how many each person gets, we di... | 9 | 9 | [
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orca_math | AI-MO/NuminaMath-CoT | null | She estimated the number of candies that she will receive from each block. If she will receive around 7 pieces of candies from every house, and there are some houses in a block, she will receive 35 candies from each block. How many houses are in a block? | If she receives 7 pieces of candies from every house and ends up with 35 candies from each block, we can find the number of houses in a block by dividing the total number of candies by the number of candies received from each house.
35 candies ÷ 7 candies/house = 5 houses
So, there are $\boxed{5}$ houses in a block. | 5 | 5 | [
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gsm8k | AI-MO/NuminaMath-CoT | null | Stacy has 2 more than triple as many berries as Steve. Steve has one half as many berries as Skylar. If Skylar has 20 berries, how many berries does Stacy have? | Given that Skylar has 20 berries, we can calculate the number of berries Steve has as follows:
Steve has = $\frac{1}{2} \times 20 = 10$ berries.
Next, we calculate the number of berries Stacy has based on the information that she has 2 more than triple the number of berries Steve has:
Stacy has = $2 + 3 \times 10 = ... | 32 | 32 | [
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orca_math | AI-MO/NuminaMath-CoT | null | James has 28 marbles. He puts them into 4 bags. He puts the same number in each bag. He then gives away some bags. James has 21 marbles left. How many bags did James give away? | If James has 28 marbles and puts them into 4 bags with the same number in each bag, then each bag would have 28 / 4 = 7 marbles.
If James has 21 marbles left, then he has given away 28 - 21 = 7 marbles.
Since each bag contains 7 marbles, and he has given away 7 marbles, that means he has given away 7 / 7 = 1 bag.
S... | 1 | 1 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Mom, Dad, and Grandpa bought clothes at the department store. Dad bought more clothes than Mom, and Grandpa bought more clothes than Dad. If you lined up people based on the number of clothes they bought in ascending order, in what position will Mom be? Please answer using an natural number. | $\boxed{1}$ | 1 | 1 | [
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orca_math | AI-MO/NuminaMath-CoT | null | The Ferris wheel in paradise park has 3 small seats and 7 large seats. Each small seat can hold 16 people and each large seat can hold 12 people. How many people can ride the Ferris wheel on large seats? | To find out how many people can ride the Ferris wheel on large seats, we need to multiply the number of large seats by the number of people each large seat can hold.
Number of large seats = 7
Number of people each large seat can hold = 12
Total number of people that can ride on large seats = Number of large seats × N... | 84 | 84 | [
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synthetic_math | AI-MO/NuminaMath-CoT | null | We have that $3a + 2 = 2$ and $b - 2a = 3.$ What is the value of $b$? | 1. Start by solving the equation $3a + 2 = 2$ for $a$:
\[
3a + 2 = 2 \implies 3a = 2 - 2 \implies 3a = 0 \implies a = 0
\]
2. Now use the equation $b - 2a = 3$:
\[
b - 2 \cdot 0 = 3 \implies b = 3
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3. Therefore, the value of $b$ is $\boxed{3}$. | 3 | 3 | [
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orca_math | AI-MO/NuminaMath-CoT | null | A pet shelter had 10 puppies when another 15 were brought in. If 7 puppies a day are adopted, how long would it take for all of them to be adopted? | The pet shelter initially had 10 puppies, and another 15 were brought in, making a total of 10 + 15 = 25 puppies.
If 7 puppies are adopted each day, we can divide the total number of puppies by the number of puppies adopted per day to find out how many days it would take for all of them to be adopted.
25 puppies ÷ 7 ... | 4 | 4 | [
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orca_math | AI-MO/NuminaMath-CoT | null | A chef served 3 different foods for a banquet: 25 plates of lobster rolls, 14 plates of spicy hot noodles, and some plates of seafood noodles. The chef made 55 plates of food altogether. How many plates of seafood noodles did the chef make? | To find out how many plates of seafood noodles the chef made, we need to subtract the number of plates of lobster rolls and spicy hot noodles from the total number of plates of food.
Total plates of food = 55
Plates of lobster rolls = 25
Plates of spicy hot noodles = 14
Plates of seafood noodles = Total plates of foo... | 16 | 16 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Edward was trying to expand his game collection. He bought 41 games from a friend and bought 14 more at a garage sale. If 31 of the games didn't work, how many good games did he end up with? | Edward bought a total of 41 games from a friend and 14 games from a garage sale, which adds up to 41 + 14 = 55 games.
If 31 of these games didn't work, then the number of good games he ended up with is the total number of games minus the number of games that didn't work: 55 - 31 = $\boxed{24}$ good games. | 24 | 24 | [
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orca_math | AI-MO/NuminaMath-CoT | null | In a football game, wristbands were given to every spectator for both their hands. In total 234 wristbands were distributed. How many people watched the game? | If every spectator received wristbands for both their hands, that means each person received 2 wristbands. To find out how many people watched the game, we divide the total number of wristbands by the number of wristbands per person.
Total wristbands = 234
Wristbands per person = 2
Number of people = Total wristbands... | 117 | 117 | [
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synthetic_math | AI-MO/NuminaMath-CoT | null | Compute: $12 \cdot \frac{1}{15} \cdot 30.$ | Start by simplifying the expression:
\[12 \cdot \frac{1}{15} \cdot 30 = 12 \cdot \left(\frac{30}{15}\right) = 12 \cdot 2\]
Now, multiply the resulting integers:
\[12 \cdot 2 = \boxed{24}\] | 24 | 24 | [
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orca_math | AI-MO/NuminaMath-CoT | null | A train 500 m long can cross an electric pole in 20 seconds. Find the speed of the train. | To find the speed of the train, we can use the formula:
Speed = Distance / Time
The distance the train covers when crossing the electric pole is equal to the length of the train, which is 500 meters. The time taken to cross the pole is given as 20 seconds.
So, plugging in the values, we get:
Speed = 500 meters / 20... | 25 | 25 | [
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synthetic_math | AI-MO/NuminaMath-CoT | null | The Ponde family's Powerjet pumps 500 gallons of water per hour. At this rate, how many gallons of water will it pump in 30 minutes? | To solve this, start by converting minutes into a fraction of an hour since the rate is given per hour. Thus, 30 minutes is $\frac{30}{60} = \frac{1}{2}$ of an hour.
Next, calculate the volume of water pumped in this duration:
\[ 500 \text{ gallons per hour} \times \frac{1}{2} \text{ hour} = 500 \times \frac{1}{2} = 2... | 250 | 250 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Eric has a chicken farm with some chickens. His chickens lay 3 eggs each day. After 3 days, Eric collected 36 eggs. How many chickens does Eric have on his farm? | If Eric collected 36 eggs after 3 days, we can calculate the number of eggs laid per day by dividing the total number of eggs by the number of days:
36 eggs / 3 days = 12 eggs per day
Since each chicken lays 3 eggs each day, we can find out the number of chickens by dividing the number of eggs laid per day by the num... | 4 | 4 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Will was organizing his baseball cards in a binder with 3 on each page. He had 8 new cards and 10 old cards to put in the binder. How many pages would he use? | Will has a total of 8 new cards + 10 old cards = 18 cards to put in the binder.
Since he can put 3 cards on each page, we divide the total number of cards by the number of cards per page to find out how many pages he will use:
18 cards ÷ 3 cards per page = 6 pages
Will would use $\boxed{6}$ pages to organize his ba... | 6 | 6 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Marcella has 27 pairs of shoes. If she loses some individual shoes, the greatest number of matching pairs she could have left is 22. How many individual shoes did she lose? | If Marcella has 27 pairs of shoes, she has a total of 27 * 2 = 54 individual shoes.
If the greatest number of matching pairs she could have left is 22, then she has 22 * 2 = 44 individual shoes that are still in pairs.
To find out how many individual shoes she lost, we subtract the number of individual shoes that are... | 10 | 10 | [
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orca_math | AI-MO/NuminaMath-CoT | null | When five is added to three more than a certain number, the result is 19. What is the number? | Let's call the certain number "x". According to the problem, we have:
5 + (x + 3) = 19
Now, let's solve for x:
5 + x + 3 = 19
x + 8 = 19
x = 19 - 8
x = 11
So, the certain number is $\boxed{11}$ . | 11 | 11 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Mrs. Wong had 30 Valentines. She gave 8 Valentines to her children, 5 Valentines to her neighbors, and 3 Valentines to her coworkers. How many Valentines does she have left? | Mrs. Wong started with 30 Valentines. She gave away:
8 Valentines to her children
5 Valentines to her neighbors
3 Valentines to her coworkers
To find out how many Valentines she has left, we need to subtract the total number of Valentines she gave away from the original amount.
Total Valentines given away = 8 + 5 + ... | 14 | 14 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Tim's cat had kittens. He gave 3 to Jessica and 6 to Sara. He now has 9 kittens. How many kittens did he have to start with? | Tim gave away a total of 3 kittens to Jessica and 6 kittens to Sara, which adds up to 3 + 6 = 9 kittens.
After giving away the kittens, Tim has 9 kittens left.
To find out how many kittens he had to start with, we add the number of kittens he gave away to the number of kittens he has left: 9 (kittens given away) + 9 ... | 18 | 18 | [
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synthetic_math | AI-MO/NuminaMath-CoT | null | A hockey league has 10 teams. During the season, each of the 10 teams plays exactly four games with each of the other teams. How many total games are played in the season? | - Calculate the number of unique game pairings among the 10 teams. Since each game involves a pair of teams, we are looking for the number of combinations of 10 teams taken 2 at a time:
\[
\binom{10}{2} = \frac{10 \times 9}{2} = 45
\]
- Each pair of teams plays four games. Therefore, the total number of games pla... | 180 | 180 | [
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synthetic_math | AI-MO/NuminaMath-CoT | null | How many matches will be held during a 10-person round-robin tennis tournament where each player plays every other player exactly once? | Let's consider n=10 as the number of players in the tournament.
- Each player will play against each other player exactly once, therefore each player plays $n - 1 = 10 - 1 = 9$ matches.
- Reasoning similarly, to count all matches without duplication, we consider the fact that each match is counted twice when summing up... | 45 | 45 | [
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gsm8k | AI-MO/NuminaMath-CoT | null | Every time Carl earned $0.50 he would go to the corner market and buy a candy bar. Carl's neighbor said he would pay him $0.75 every week for taking out his trash. At the end of four weeks, how many candy bars will Carl be able to buy? | To determine how many candy bars Carl can buy after four weeks, we need to follow these steps:
1. Calculate the total amount Carl earned in four weeks. Since Carl is paid $0.75 every week for taking out his neighbor's trash, over four weeks, he earns:
\[
0.75 \times 4 = \$3.00
\]
So, Carl made a total of $... | 6 | 6 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Phoebe eats 1 serving and gives her dog 1 serving of peanut butter for a bedtime snack. Each jar of peanut butter has 15 servings. She needs a certain number of jars to make sure she and her dog have enough to last for a specific number of days. If she needs 4 jars, how many days will the peanut butter last? | Phoebe and her dog together consume 2 servings of peanut butter per day (1 serving each).
If each jar has 15 servings, then 4 jars will have a total of 4 jars * 15 servings/jar = 60 servings.
Since they consume 2 servings per day, the peanut butter will last for 60 servings / 2 servings per day = $\boxed{30}$ days. | 30 | 30 | [
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orca_math | AI-MO/NuminaMath-CoT | null | In a division sum, the remainder is 0. A student mistook the divisor by 12 instead of 21 and obtained some quotient. The correct quotient is 20. What quotient did the student obtain by mistake? | Let's denote the dividend (the number being divided) as D, the correct divisor as 21, and the mistaken divisor as 12.
Since the remainder is 0 when the correct divisor is used, we know that D is exactly divisible by 21. Therefore, we can write:
D = 21 * Correct Quotient
Given that the correct quotient is 20, we can ... | 35 | 35 | [
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orca_math | AI-MO/NuminaMath-CoT | null | A new building needed 9 windows. The builder had already installed 6 of them. It takes a certain amount of time to install each window, and it will take him 18 hours to install the rest. How long does it take to install one window? | The builder has 3 windows left to install, and it will take him 18 hours to install them. To find out how long it takes to install one window, we divide the total time by the number of windows left to install.
18 hours ÷ 3 windows = 6 hours per window
So, it takes $\boxed{6}$ hours to install one window. | 6 | 6 | [
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gsm8k | AI-MO/NuminaMath-CoT | null | Tom and Tim both brought 4, six-sided dice to school. How many total sides are there? | To solve the problem, we start by calculating the total number of dice Tom and Tim brought to school. Since both Tom and Tim brought 4 six-sided dice each, we add the number of dice each brought:
\[4 \text{ (Tom's dice)} + 4 \text{ (Tim's dice)} = 8 \text{ total dice}\]
Next, we need to find the total number of sides... | 48 | 48 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Faye and her mom were picking carrots from their garden. Faye picked 23 carrots and her mother picked some. If only 12 of the carrots were good, and they had 16 bad carrots, how many carrots did her mother pick? | Faye and her mother picked a total of 12 good carrots and 16 bad carrots, which adds up to 12 + 16 = 28 carrots.
Since Faye picked 23 carrots, her mother must have picked the remaining number of carrots. So, her mother picked 28 - 23 = $\boxed{5}$ carrots. | 5 | 5 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Nancy has 7 black balloons. Mary has 4 times more black balloons than Nancy. Mary have _____ black balloons now . | If Mary has 4 times more black balloons than Nancy, and Nancy has 7 black balloons, then Mary has:
7 balloons (Nancy's amount) * 4 = 28 balloons
Mary has $\boxed{28}$ black balloons now. | 28 | 28 | [
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synthetic_math | AI-MO/NuminaMath-CoT | null | Determine the sixth term of the geometric sequence with the first term $3$ and the second term $6$. | 1. **Find the common ratio**: The common ratio, $r$, is the quotient of the second term by the first term. Thus,
\[
r = \frac{6}{3} = 2.
\]
2. **General formula for the $k^{th}$ term**: The $k^{th}$ term of a geometric sequence can be found using the formula $a_k = a \cdot r^{k-1}$, where $a$ is the first ter... | 96 | 96 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Melanie had 7 dimes in her bank. Her dad gave her some dimes and her mother gave her 4 dimes. Now, Melanie has 19 dimes. How many dimes did her dad give her? | Melanie originally had 7 dimes. Her mother gave her 4 more dimes, so that adds up to 7 + 4 = 11 dimes.
Now, Melanie has a total of 19 dimes. To find out how many dimes her dad gave her, we subtract the number of dimes she had after her mother gave her some from the total number of dimes she has now:
19 (total dimes) ... | 8 | 8 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Alex had some ounces of jelly beans. He ate 6 ounces. Then he divided the rest equally into 3 piles, and each pile weighs 10 ounces. How many ounces of jelly beans did Alex have initially? | If Alex divided the remaining jelly beans into 3 piles of 10 ounces each, then the total weight of the remaining jelly beans is 3 piles * 10 ounces/pile = 30 ounces.
Since Alex ate 6 ounces before dividing the jelly beans, we need to add those 6 ounces back to the remaining amount to find the initial weight.
So, the ... | 36 | 36 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Every week, Lucas makes 4 pieces of chocolate candy for each of his students on Monday. This upcoming Monday, 3 of Lucas' students will not be coming to class, and he will make 28 pieces of chocolate candy. How many pieces of chocolate candy did Lucas make for his class last Monday? | Let's denote the number of students Lucas has as S. Since 3 students will not be coming this upcoming Monday, he will be making chocolate candy for S - 3 students. We know that he will make 28 pieces of chocolate candy for S - 3 students, and he makes 4 pieces per student. So we can write the equation:
4 * (S - 3) = 2... | 40 | 40 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Jared likes to draw monsters. He drew a monster family portrait. The mom had 1 eye, the dad had some eyes, and they had 3 kids, each with 4 eyes. The whole family had 16 eyes. How many eyes did the dad have? | Let's calculate the total number of eyes for the family members we know:
- The mom has 1 eye.
- The 3 kids have 4 eyes each, so that's 3 kids * 4 eyes = 12 eyes.
Now, let's add the mom's and the kids' eyes together:
1 eye (mom) + 12 eyes (kids) = 13 eyes.
We know the whole family has 16 eyes, so to find out how man... | 3 | 3 | [
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orca_math | AI-MO/NuminaMath-CoT | null | The average of 10 numbers was calculated as a certain value. It is discovered later on that while calculating the average, one number, namely 66, was incorrectly read as 26. The correct average is 22. What was the initially calculated average? | Let's denote the sum of the 10 numbers as S. The initially calculated average A1 is given by:
A1 = S / 10
It is given that the correct average A2 is 22, so the correct sum S2 of the 10 numbers is:
A2 = S2 / 10
22 = S2 / 10
S2 = 22 * 10
S2 = 220
The incorrect sum S1 (which was used to calculate the initially incorre... | 26 | 26 | [
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cn_k12 | AI-MO/NuminaMath-CoT | null | Calculate: $-3 + 2 = \quad$; $\quad (-3) \times 2 = \quad$. | For the first part, $-3 + 2$, we simply add the numbers considering their signs. Since $-3$ is negative and $2$ is positive, we subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value number, which gives us $-1$. Therefore, the answer to the first part is $\boxed{-1}$.
Fo... | -6 | -6 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Shane wants to take as many photos as possible this year. He takes 146 photos in the first 2 months of the year. In January, he takes some photos every day. In February, he took 21 photos each week. How many photos did Shane take each day in January? | Let's break down the information given:
- Shane takes 146 photos in the first 2 months of the year.
- In February, he took 21 photos each week.
First, let's find out how many photos Shane took in February. Since February typically has 4 weeks, we multiply the number of photos taken each week by the number of weeks:
... | 2 | 2 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Noa scored some points to win a bowl, and Phillip scores twice that number. The total number of points Noa and Phillip scored to win the bowl is 90. How many points did Noa score? | Let's denote the number of points Noa scored as N. According to the problem, Phillip scored twice the number of points that Noa scored, so Phillip's score is 2N.
The total number of points scored by Noa and Phillip is given as 90. Therefore, we can write the equation:
N + 2N = 90
Combining like terms, we get:
3N = ... | 30 | 30 | [
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orca_math | AI-MO/NuminaMath-CoT | null | The average marks of 25 students in a class is 100. A student's mark is wrongly noted as a certain value instead of 10. The correct average marks is 98. What was the wrongly noted mark of the student? | Let's denote the wrongly noted mark as x.
The sum of the marks of all 25 students with the wrong mark is:
25 * 100 = 2500
If we replace the wrongly noted mark with the correct mark (10), the sum of the marks should be:
2500 - x + 10
The correct average marks for the 25 students is 98, so the correct sum of the marks... | 60 | 60 | [
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orca_math | AI-MO/NuminaMath-CoT | null | John with his five friends ordered 3 pizzas. Each pizza had a certain number of slices. They all finished and ate the same amount of pizzas, and each person ate 4 slices. How many slices did each pizza have? | If John and his five friends all ate the same amount of pizza, and each person ate 4 slices, then we can calculate the total number of slices eaten by multiplying the number of people by the number of slices each person ate.
John + 5 friends = 6 people
Each person ate 4 slices.
Total slices eaten = 6 people * 4 slice... | 8 | 8 | [
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synthetic_math | AI-MO/NuminaMath-CoT | null | Calculate $4 \cdot 6 \cdot 8 + 24 \div 4.$ | Following the rule of order of operations (PEMDAS/BODMAS), we first handle the multiplication and division inside the expression before performing any additional operations.
1. Perform the multiplication:
\[
4 \cdot 6 \cdot 8 = 24 \cdot 8 = 192.
\]
2. Perform the division:
\[
24 \div 4 = 6.
\]
3. Add... | 198 | 198 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Jeongho's farm has chickens and pigs. If the sum of all the legs is 48, and there are 9 pigs, how many chickens are there on the farm? | Let's denote the number of chickens as C and the number of pigs as P. We know that P = 9.
Each chicken has 2 legs, and each pig has 4 legs. The total number of legs is given as 48.
The equation for the total number of legs is:
2 * C (chickens' legs) + 4 * P (pigs' legs) = 48
We know the number of pigs (P = 9), so we... | 6 | 6 | [
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synthetic_math | AI-MO/NuminaMath-CoT | null | At Northstar High School, the 120 students who participate in the Math Club usually meet to discuss various topics and enjoy some snacks. This year, Daniel and Emily are in charge of baking the cookies. They follow a recipe that makes a batch of 18 cookies using the following ingredients:
- 2 cups of flour
- 2.5 eggs
... | 1. Calculate the new number of students expected to attend:
\[ 120 \times (1 - 0.30) = 120 \times 0.70 = 84 \]
2. Determine the total number of cookies needed (3 cookies per student):
\[ 84 \times 3 = 252 \]
3. Find out how many full recipes are required (each recipe makes 18 cookies):
\[ \frac{252}{18} = 14... | 14 | 14 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Joan decided to sell all of her old books. She gathered up 75 books to sell. She sold 33 books in a yard sale, and decided to sell the rest on an online platform. On the first day, she managed to sell 15 books online and on the following two days, she sold 8 books and 12 books respectively. Joan has _____ books now. | Joan started with 75 books. She sold 33 books in a yard sale, so she had 75 - 33 = 42 books left to sell online.
On the first day, she sold 15 books online, so she had 42 - 15 = 27 books left.
On the second day, she sold 8 books, so she had 27 - 8 = 19 books left.
On the third day, she sold 12 books, so she had 19 -... | 7 | 7 | [
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orca_math | AI-MO/NuminaMath-CoT | null | In a school of 850 boys, 40% are Muslims, 28% are Hindus, 10% are Sikhs, and the remaining belong to other communities. How many boys belong to other communities? | To find out how many boys belong to other communities, we first need to calculate the total percentage of boys who are Muslims, Hindus, and Sikhs. Then we subtract this from 100% to find the percentage of boys who belong to other communities.
Percentage of Muslims: 40%
Percentage of Hindus: 28%
Percentage of Sikhs: 10... | 187 | 187 | [
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synthetic_math | AI-MO/NuminaMath-CoT | null | Compute $(142 + 29 + 26 + 14) \times 2$. | First, perform the additions inside the parenthesis:
- $142 + 29 = 171$
- $26 + 14 = 40$
- Now add these two results: $171 + 40 = 211$
Next, multiply the sum by 2:
- $211 \times 2 = 422$
Thus, the computed result is $\boxed{422}$. | 422 | 422 | [
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orca_math | AI-MO/NuminaMath-CoT | null | 14 is what percent of 70? | To find what percent 14 is of 70, you can use the following formula:
Percent = (Part / Whole) * 100
In this case, the "Part" is 14 and the "Whole" is 70. So you would calculate:
Percent = (14 / 70) * 100
Percent = 0.2 * 100
Percent = 20
So, 14 is $\boxed{20}$ percent of 70. | 20 | 20 | [
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orca_math | AI-MO/NuminaMath-CoT | null | How many diagonals can be drawn in the figure below? : Pentadecagon | A pentadecagon is a polygon with 15 sides. To find the number of diagonals in any polygon, you can use the formula:
Number of diagonals = n(n - 3) / 2
where n is the number of sides in the polygon.
For a pentadecagon, n = 15. Plugging this into the formula:
Number of diagonals = 15(15 - 3) / 2
Number of diagonals =... | 90 | 90 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Kiarra is twice as old as Bea. Job is 3 times older than Bea. Figaro is 7 years older than Job. Harry is half as old as Figaro. If Harry is 26, how old is Kiarra? | If Harry is 26 years old and he is half as old as Figaro, then Figaro is twice Harry's age. So, Figaro's age is:
Figaro = 2 * Harry
Figaro = 2 * 26
Figaro = 52 years old
Since Figaro is 7 years older than Job, we can find Job's age by subtracting 7 from Figaro's age:
Job = Figaro - 7
Job = 52 - 7
Job = 45 years old
... | 30 | 30 | [
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orca_math | AI-MO/NuminaMath-CoT | null | The average weight of 8 persons increases by 4 kg when a new person comes in place of one of them weighing 55 kg. What might be the weight of the new person? | Let's denote the weight of the new person as W.
The total weight increase for the group of 8 persons is 8 persons * 4 kg/person = 32 kg.
This increase is due to the replacement of the person who weighs 55 kg with the new person. Therefore, the weight of the new person must be 55 kg + 32 kg to account for the total we... | 87 | 87 | [
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orca_math | AI-MO/NuminaMath-CoT | null | a 21 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ? | Let's call the length of the shorter piece \( x \) cm. Then, the longer piece would be \( \frac{5}{2} \) times longer than the shorter piece, which is \( \frac{5}{2}x \) cm.
The total length of the wire is the sum of the lengths of the two pieces, which is 21 cm. So we can write the equation:
\[ x + \frac{5}{2}x = 21... | 6 | 6 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Adam had some quarters. He spent a certain number of them at the arcade and had seventy-nine left over. He started with 88 quarters. How many quarters did he spend at the arcade? | Adam started with 88 quarters and had 79 left after spending some at the arcade. To find out how many quarters he spent, we subtract the number of quarters he had left from the number he started with:
88 quarters (started with) - 79 quarters (left over) = $\boxed{9}$ quarters spent at the arcade. | 9 | 9 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Jessa needs to make cupcakes for 3 fourth-grade classes that each have 30 students and a P.E. class with a certain number of students. She needs to make 140 cupcakes. How many students are in the P.E. class? | First, let's calculate the total number of cupcakes needed for the three fourth-grade classes. Since each class has 30 students and there are 3 classes, we multiply 30 by 3:
30 students/class * 3 classes = 90 students
Now, we know that Jessa needs to make 140 cupcakes in total. We have already accounted for 90 cupcak... | 50 | 50 | [
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orca_math | AI-MO/NuminaMath-CoT | null | There is 80 mg of caffeine in a cup of coffee. Lisa does not want to drink more than 200 mg of caffeine per day. She drinks a certain number of cups of coffee and ends up drinking 40 milligrams of coffee over her goal. How many cups of coffee did Lisa drink? | Lisa drank 40 milligrams of caffeine over her goal of 200 milligrams. This means she consumed a total of 200 + 40 = 240 milligrams of caffeine.
Since each cup of coffee contains 80 milligrams of caffeine, we can calculate the number of cups she drank by dividing the total amount of caffeine she consumed by the amount ... | 3 | 3 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Sam grew 4 watermelons, but the rabbits ate some watermelons. Now, Sam has 1 watermelon left. How many watermelons did the rabbits eat? | If Sam originally had 4 watermelons and now has only 1 left, then the rabbits must have eaten:
4 (original watermelons) - 1 (remaining watermelon) = 3 watermelons
The rabbits ate $\boxed{3}$ watermelons. | 3 | 3 | [
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cn_k12 | AI-MO/NuminaMath-CoT | null | In the arithmetic sequence $\{a_n\}$, $a_2 = -5$ and $d = 3$. Find $a_1$. | Since in the arithmetic sequence $\{a_n\}$, $a_2 = -5$ and $d = 3$,
we have $a_1 + d = a_2$. Substituting the given values, we get $a_1 + 3 = -5$,
solving this equation, we find $a_1 = -8$.
Therefore, the answer is $\boxed{-8}$.
**Analysis:** The solution is obtained by using the general formula of an arithmet... | -8 | -8 | [
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orca_math | AI-MO/NuminaMath-CoT | null | If some a = 6 b = 20, then 120 ab = 800. What is the value of 10 a? | Given that a = 6 and b = 20, we can calculate the value of 120ab as follows:
120ab = 120 * a * b
120ab = 120 * 6 * 20
120ab = 720 * 20
120ab = 14400
However, you've stated that 120ab = 800, which is not correct based on the given values of a and b. There might be a mistake in the given information.
If we proceed wit... | 60 | 60 | [
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orca_math | AI-MO/NuminaMath-CoT | null | find the number of terms in an arithmetic progression with the first term 2 and the last term being 62 , given that common difference is 2 . | To find the number of terms in an arithmetic progression (AP), we can use the formula for the nth term of an AP:
\[ a_n = a_1 + (n - 1)d \]
where:
- \( a_n \) is the nth term (the last term in this case, which is 62),
- \( a_1 \) is the first term (which is 2),
- \( d \) is the common difference (which is 2),
- \( n ... | 31 | 31 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Mona brought 20 cookies to share in class. Jasmine brought fewer cookies than Mona. Rachel brought 10 more cookies than Jasmine. Mona, Jasmine, and Rachel brought altogether 60 cookies to share in class. How many cookies did Jasmine bring? | Let's denote the number of cookies Jasmine brought as J.
According to the information given:
- Mona brought 20 cookies.
- Rachel brought 10 more cookies than Jasmine, so Rachel brought J + 10 cookies.
- Together, they brought 60 cookies.
So we can write the equation:
Mona's cookies + Jasmine's cookies + Rachel's coo... | 15 | 15 | [
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orca_math | AI-MO/NuminaMath-CoT | null | In a school of 1200 students, 35% are Muslims, 25% are Hindus, 15% are Sikhs, 10% are Christians, 5% are Buddhists, and the remaining students belong to other religious communities. How many students belong to the other religious communities? | To find out how many students belong to other religious communities, we first need to calculate the percentage of students that are accounted for by the given religions:
Muslims: 35%
Hindus: 25%
Sikhs: 15%
Christians: 10%
Buddhists: 5%
Now, let's add these percentages together:
35% + 25% + 15% + 10% + 5% = 90%
This... | 120 | 120 | [
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orca_math | AI-MO/NuminaMath-CoT | null | There are some pigs in the barn. 22 more come to join them. Now there are 86 pigs. How many pigs were in the barn initially? | To find out how many pigs were in the barn initially, we can subtract the number of pigs that came to join from the total number of pigs now.
So, we do 86 (total number of pigs now) - 22 (number of pigs that joined) = 64 pigs.
There were initially $\boxed{64}$ pigs in the barn. | 64 | 64 | [
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orca_math | AI-MO/NuminaMath-CoT | null | When the shuttlecocks were distributed equally to 24 students in Yunsu's class, 19 shuttlecocks were distributed to each student and there were no shuttlecocks left. Find the total number of shuttlecocks distributed to the students in Yunsu's class. | If each of the 24 students received 19 shuttlecocks and there were none left over, then the total number of shuttlecocks distributed can be found by multiplying the number of students by the number of shuttlecocks each student received.
Total number of shuttlecocks = Number of students × Number of shuttlecocks per stu... | 456 | 456 | [
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synthetic_math | AI-MO/NuminaMath-CoT | null | Six socks, colored blue, brown, black, red, purple, and green are in a drawer. In how many different ways can we choose four socks from the drawer if the order of the socks does not matter, and at least one of the socks chosen must be blue? | 1. Number socks total = 6 (including one blue).
2. Choose 4 socks including at least one blue. Begin by choosing the blue sock (1 way), then choose 3 more from the remaining 5. Utilize combinations:
- First, choose 1 blue (1 way).
- Then choose 3 from the remaining 5 non-blue socks: $\binom{5}{3}$.
Calcula... | 10 | 10 | [
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orca_math | AI-MO/NuminaMath-CoT | null | Dana has 15 more pencils than Jayden, who has twice as much as Marcus. How many more pencils does Dana have than Marcus, if Jayden has 20 pencils? | If Jayden has 20 pencils, and Dana has 15 more pencils than Jayden, then Dana has 20 + 15 = 35 pencils.
Since Jayden has twice as many pencils as Marcus, we can find out how many pencils Marcus has by dividing the number of pencils Jayden has by 2. So, Marcus has 20 / 2 = 10 pencils.
Now, to find out how many more pe... | 25 | 25 | [
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orca_math | AI-MO/NuminaMath-CoT | null | David obtained 96 marks in English, 98 in Mathematics, 99 in Physics, some marks in Chemistry, and 98 in Biology. His average marks are 98.2. What are his marks in Chemistry? | To find David's marks in Chemistry, we first need to calculate the total marks he obtained in all subjects. Since we know his average marks, we can multiply the average by the number of subjects to get the total marks.
David's average marks = 98.2
Number of subjects = 5 (English, Mathematics, Physics, Chemistry, Biolo... | 100 | 100 | [
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synthetic_math | AI-MO/NuminaMath-CoT | null | Add $5_8 + 13_8.$ Express your answer in base $8.$ | First, convert the numbers to base $10$ if necessary for clarity:
- $5_8$ in base $10$ is $5$.
- $13_8$ in base $10$ is $1 \times 8 + 3 = 11$.
Now, add these numbers in base $10$:
\[ 5 + 11 = 16 \]
Next, convert $16$ in base $10$ back to base $8$:
- $16 \div 8 = 2$ remainder $0$, so the last digit is $0$.
- The quoti... | 20_8 | 208 | [
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orca_math | AI-MO/NuminaMath-CoT | null | What least number should be subtracted from 3,381 so that the remainder when divided by 9, 11, and 17 will leave in each case the same remainder? The answer is 7. What is the common remainder? | To find the common remainder when 3,381 is divided by 9, 11, and 17, we first subtract 7 from 3,381 to get the number that is divisible by all three numbers with the same remainder.
3,381 - 7 = 3,374
Now, we need to find the remainder when 3,374 is divided by 9, 11, and 17.
For 9:
3,374 ÷ 9 = 374 with a remainder of... | 8 | 8 | [
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orca_math | AI-MO/NuminaMath-CoT | null | She sent away a part of her rock collection to the Geological Museum in London. She was left with her 15 favorite stones after sending away 63 stones. How many stones did she originally have in her collection? | She sent away 63 stones and was left with 15 stones. To find out how many stones she originally had, we add the stones she sent away to the stones she kept:
63 stones (sent away) + 15 stones (kept) = 78 stones (original collection)
So, she originally had $\boxed{78}$ stones in her collection. | 78 | 78 | [
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