id string | reannotated_assistant_content string | problem string | source string | solution string | verified null | quality_metrics null | Thought string | Prompt string | Solution string | Solution_source string | Answer string | Source string | System string | Verifiable int64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
id_0 | <think>
First, I need to determine the total number of children on the playground by adding the number of boys and girls.
There are 27 boys and 35 girls.
Adding these together: 27 boys + 35 girls = 62 children.
Therefore, the total number of children on the playground is 62.
</think>
To find the total number of chi... | There were 27 boys and 35 girls on the playground at recess. There were _____ children on the playground at recess. | orca_math |
There were 62 children on the playground at recess. (27 boys + 35 girls = $\boxed{62}$ children) | null | null | <think>
First, I need to determine the total number of children on the playground by adding the number of boys and girls.
There are 27 boys and 35 girls.
Adding these together: 27 boys + 35 girls = 62 children.
Therefore, the total number of children on the playground is 62.
</think>
To find the total number of chi... | 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) |
There were 62 children on the playground at recess. (27 boys + 35 girls = $\boxed{62}$ children) | 62 | R1-Distill-SFT | 1 | |
id_1 | <think>
First, I need to determine the cost per dozen oranges. John bought three dozen oranges for \$28.80, so I can find the cost per dozen by dividing the total cost by the number of dozens.
Next, with the cost per dozen known, I can calculate the cost for five dozen oranges by multiplying the cost per dozen by five... | John purchased three dozen oranges for $\$$28.80. At the same rate, how much would five dozen of these oranges cost? | synthetic_math | The problem states that John bought three dozen oranges for $\$$28.80. To find the cost per dozen, we use the formula:
$$ \text{Cost per dozen} = \frac{\text{Total cost}}{\text{Number of dozens}} = \frac{\$28.80}{3} = \$9.60 \text{ per dozen}. $$
To determine the cost for five dozen oranges:
$$ \text{Cost for five doz... | null | null | <think>
First, I need to determine the cost per dozen oranges. John bought three dozen oranges for \$28.80, so I can find the cost per dozen by dividing the total cost by the number of dozens.
Next, with the cost per dozen known, I can calculate the cost for five dozen oranges by multiplying the cost per dozen by five... | John purchased three dozen oranges for $\$$28.80. At the same rate, how much would five dozen of these oranges cost? | The problem states that John bought three dozen oranges for $\$$28.80. To find the cost per dozen, we use the formula:
$$ \text{Cost per dozen} = \frac{\text{Total cost}}{\text{Number of dozens}} = \frac{\$28.80}{3} = \$9.60 \text{ per dozen}. $$
To determine the cost for five dozen oranges:
$$ \text{Cost for five doz... | The problem states that John bought three dozen oranges for $\$$28.80. To find the cost per dozen, we use the formula:
$$ \text{Cost per dozen} = \frac{\text{Total cost}}{\text{Number of dozens}} = \frac{\$28.80}{3} = \$9.60 \text{ per dozen}. $$
To determine the cost for five dozen oranges:
$$ \text{Cost for five doz... | \$48 | R1-Distill-SFT | 1 | |
id_2 | <think>
First, determine how many bags Bianca actually recycled by subtracting the number of bags she did not recycle from the total number of bags she had.
Then, calculate the total points she earned by multiplying the number of recycled bags by the points earned per bag.
</think>
**Solution:**
1. **Determine the n... | 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? | orca_math | 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. | null | null | <think>
First, determine how many bags Bianca actually recycled by subtracting the number of bags she did not recycle from the total number of bags she had.
Then, calculate the total points she earned by multiplying the number of recycled bags by the points earned per bag.
</think>
**Solution:**
1. **Determine the n... | 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. | 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 | R1-Distill-SFT | 1 | |
id_3 | <think>
First, identify the cost of one bottle cap, which is $2.
Next, determine the number of bottle caps needed, which is 6.
Multiply the cost per bottle cap by the number of bottle caps: 6 × $2 = $12.
Therefore, the total cost for 6 bottle caps is $12.
</think>
To determine the total cost of 6 bottle caps, follo... | Each bottle cap costs $2. How much do 6 bottle caps cost? | orca_math |
If each bottle cap costs $2, then 6 bottle caps would cost 6 x $2 = $\boxed{\$12}$ . | null | null | <think>
First, identify the cost of one bottle cap, which is $2.
Next, determine the number of bottle caps needed, which is 6.
Multiply the cost per bottle cap by the number of bottle caps: 6 × $2 = $12.
Therefore, the total cost for 6 bottle caps is $12.
</think>
To determine the total cost of 6 bottle caps, follo... | Each bottle cap costs $2. How much do 6 bottle caps cost? |
If each bottle cap costs $2, then 6 bottle caps would cost 6 x $2 = $\boxed{\$12}$ . |
If each bottle cap costs $2, then 6 bottle caps would cost 6 x $2 = $\boxed{\$12}$ . | \$12 | R1-Distill-SFT | 1 | |
id_4 | <think>
First, I need to determine how many emails Jack received in the afternoon.
I know that Jack received 6 emails in the morning.
It is also given that he received 2 more emails in the afternoon than in the morning.
To find the total number of emails received in the afternoon, I will add the number of emails rec... | 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? | orca_math |
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. | null | null | <think>
First, I need to determine how many emails Jack received in the afternoon.
I know that Jack received 6 emails in the morning.
It is also given that he received 2 more emails in the afternoon than in the morning.
To find the total number of emails received in the afternoon, I will add the number of emails rec... | 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. |
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 | R1-Distill-SFT | 1 | |
id_5 | <think>
First, I need to determine the number of apples and oranges Leif has.
Leif has 14 apples.
He also has 2 dozen oranges. Since 1 dozen equals 12, 2 dozen equals 24 oranges.
To find out how many more oranges he has than apples, I subtract the number of apples from the number of oranges.
24 oranges minus 14 app... | Leif’s apple tree has 14 apples and his orange tree has 2 dozen oranges. How many more oranges does he have than apples? | orca_math | 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. | null | null | <think>
First, I need to determine the number of apples and oranges Leif has.
Leif has 14 apples.
He also has 2 dozen oranges. Since 1 dozen equals 12, 2 dozen equals 24 oranges.
To find out how many more oranges he has than apples, I subtract the number of apples from the number of oranges.
24 oranges minus 14 app... | 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. | 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 | R1-Distill-SFT | 1 | |
id_6 | <think>
First, I recognize that π is a well-known mathematical constant approximately equal to 3.141592653589793.
Next, I compare this value to 3.14. By examining the decimal places, I see that 3.141592653589793 is greater than 3.14.
Therefore, I conclude that π is greater than 3.14.
</think>
To compare the sizes of... | Compare the sizes: $\pi$ ____ $3.14$ (fill in the blank with $=$, $>$, or $<$). | cn_k12 | To compare the sizes of $\pi$ and $3.14$, we start by noting the approximate value of $\pi$:
$\pi \approx 3.1415$
Then, we compare this approximation to $3.14$:
$3.1415 > 3.14$
Therefore, it follows that:
$\pi > 3.14$
So, for the blank, we fill in with the symbol $>$, encapsulating the final answer as:
$\boxed{>... | null | null | <think>
First, I recognize that π is a well-known mathematical constant approximately equal to 3.141592653589793.
Next, I compare this value to 3.14. By examining the decimal places, I see that 3.141592653589793 is greater than 3.14.
Therefore, I conclude that π is greater than 3.14.
</think>
To compare the sizes of... | Compare the sizes: $\pi$ ____ $3.14$ (fill in the blank with $=$, $>$, or $<$). | To compare the sizes of $\pi$ and $3.14$, we start by noting the approximate value of $\pi$:
$\pi \approx 3.1415$
Then, we compare this approximation to $3.14$:
$3.1415 > 3.14$
Therefore, it follows that:
$\pi > 3.14$
So, for the blank, we fill in with the symbol $>$, encapsulating the final answer as:
$\boxed{>... | To compare the sizes of $\pi$ and $3.14$, we start by noting the approximate value of $\pi$:
$\pi \approx 3.1415$
Then, we compare this approximation to $3.14$:
$3.1415 > 3.14$
Therefore, it follows that:
$\pi > 3.14$
So, for the blank, we fill in with the symbol $>$, encapsulating the final answer as:
$\boxed{>... | > | R1-Distill-SFT | 1 | |
id_7 | <think>
First, I need to determine the number of diagonals in a rectangle. A rectangle has four sides, and each vertex connects to two non-adjacent vertices, resulting in two diagonals.
Next, I will add 3 to the number of diagonals. So, 2 diagonals plus 3 equals 5.
Therefore, the final value after adding 3 to the num... | Find the value of adding 3 to the number of diagonals in the rectangle. | orca_math | 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 $\boxed{5}$ . | null | null | <think>
First, I need to determine the number of diagonals in a rectangle. A rectangle has four sides, and each vertex connects to two non-adjacent vertices, resulting in two diagonals.
Next, I will add 3 to the number of diagonals. So, 2 diagonals plus 3 equals 5.
Therefore, the final value after adding 3 to the num... | 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 $\boxed{5}$ . | 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 | R1-Distill-SFT | 1 | |
id_8 | <think>
First, I need to determine the number of male animals. Since males outnumber females by 7, I can calculate the number of males by adding 7 to the number of females.
Next, I will add the number of female animals to the number of male animals to find the total number of animals in the zoo.
</think>
**Solution:*... | The zoo keeps 35 female (a) animals. Males outnumber females by 7. How many (a) animals are there in all? | orca_math | 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. | null | null | <think>
First, I need to determine the number of male animals. Since males outnumber females by 7, I can calculate the number of males by adding 7 to the number of females.
Next, I will add the number of female animals to the number of male animals to find the total number of animals in the zoo.
</think>
**Solution:*... | 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. | 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 | R1-Distill-SFT | 1 | |
id_9 | <think>
First, determine the number of red marbles Jessica has by calculating 3 dozen, which equals 3 multiplied by 12.
Next, calculate how many times more red marbles Sandy has compared to Jessica by multiplying Jessica's total by 4.
Finally, present the result as the total number of red marbles Sandy has.
</think>
... | Jessica has 3 dozen red marbles. Sandy has 4 times more red marbles than Jessica. How many red marbles does Sandy have? | orca_math | 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. | null | null | <think>
First, determine the number of red marbles Jessica has by calculating 3 dozen, which equals 3 multiplied by 12.
Next, calculate how many times more red marbles Sandy has compared to Jessica by multiplying Jessica's total by 4.
Finally, present the result as the total number of red marbles Sandy has.
</think>
... | 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. | 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 | R1-Distill-SFT | 1 | |
id_10 | <think>
First, I need to determine Marguerite's average speed by dividing the distance she drove by the time she took.
Next, I'll use this average speed to calculate how many miles Sam drove by multiplying the speed by the time he spent driving.
Finally, I'll present the calculated distance that Sam drove.
</think>
... | Marguerite drove 150 miles in 3 hours. If Sam drove for 4.5 hours at the same average rate as Marguerite, how many miles did he drive? | synthetic_math | First, calculate Marguerite’s average speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{150 \text{ miles}}{3 \text{ hours}} = 50 \text{ mph} \]
Since Sam drove at the same average speed for 4.5 hours, the distance he traveled is calculated as:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 5... | null | null | <think>
First, I need to determine Marguerite's average speed by dividing the distance she drove by the time she took.
Next, I'll use this average speed to calculate how many miles Sam drove by multiplying the speed by the time he spent driving.
Finally, I'll present the calculated distance that Sam drove.
</think>
... | Marguerite drove 150 miles in 3 hours. If Sam drove for 4.5 hours at the same average rate as Marguerite, how many miles did he drive? | First, calculate Marguerite’s average speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{150 \text{ miles}}{3 \text{ hours}} = 50 \text{ mph} \]
Since Sam drove at the same average speed for 4.5 hours, the distance he traveled is calculated as:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 5... | First, calculate Marguerite’s average speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{150 \text{ miles}}{3 \text{ hours}} = 50 \text{ mph} \]
Since Sam drove at the same average speed for 4.5 hours, the distance he traveled is calculated as:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 5... | 225 \text{ miles | R1-Distill-SFT | 1 | |
id_11 | <think>
First, I need to determine how many days the Sumata family spent on their vacation. They drove a total of 1250 miles and covered 250 miles each day.
To find the number of days, I will divide the total miles driven by the miles driven each day.
So, 1250 miles divided by 250 miles per day equals 5 days.
Theref... | 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? | orca_math | 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 ... | null | null | <think>
First, I need to determine how many days the Sumata family spent on their vacation. They drove a total of 1250 miles and covered 250 miles each day.
To find the number of days, I will divide the total miles driven by the miles driven each day.
So, 1250 miles divided by 250 miles per day equals 5 days.
Theref... | 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 ... | 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 | R1-Distill-SFT | 1 | |
id_12 | <think>
First, I note that Eugene initially has 51.0 pencils.
After giving some pencils to Joyce, Eugene has 45 pencils remaining.
To find out how many pencils Eugene gave to Joyce, I subtract the number of pencils he has left from the initial number of pencils he had.
So, 51.0 pencils minus 45 pencils equals 6 penc... | Eugene has 51.0 pencils. He gives some pencils to Joyce and has 45 pencils left. How many pencils did Eugene give to Joyce? | orca_math | 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 $... | null | null | <think>
First, I note that Eugene initially has 51.0 pencils.
After giving some pencils to Joyce, Eugene has 45 pencils remaining.
To find out how many pencils Eugene gave to Joyce, I subtract the number of pencils he has left from the initial number of pencils he had.
So, 51.0 pencils minus 45 pencils equals 6 penc... | 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 $... | 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 | R1-Distill-SFT | 1 | |
id_13 | <think>
First, I note that there are initially 2 birds and 6 storks on the fence.
Then, 3 more birds join them, increasing the total number of birds to 2 + 3 = 5 birds.
To find out how many more storks there are compared to birds, I subtract the number of birds from the number of storks: 6 storks - 5 birds = 1 more s... | 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? | orca_math | 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... | null | null | <think>
First, I note that there are initially 2 birds and 6 storks on the fence.
Then, 3 more birds join them, increasing the total number of birds to 2 + 3 = 5 birds.
To find out how many more storks there are compared to birds, I subtract the number of birds from the number of storks: 6 storks - 5 birds = 1 more s... | 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... | 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 | R1-Distill-SFT | 1 | |
id_14 | <think>
First, I need to determine the total number of pieces of candy Sarah received. She got 66 pieces from her neighbors and 15 pieces from her older sister.
Next, I'll add these two amounts together to find the total number of candies:
66 (from neighbors) + 15 (from sister) = 81 pieces of candy
Sarah ate these c... | 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? | orca_math | 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... | null | null | <think>
First, I need to determine the total number of pieces of candy Sarah received. She got 66 pieces from her neighbors and 15 pieces from her older sister.
Next, I'll add these two amounts together to find the total number of candies:
66 (from neighbors) + 15 (from sister) = 81 pieces of candy
Sarah ate these c... | 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... | 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 | R1-Distill-SFT | 1 | |
id_15 | <think>
First, I identify the number of dimes Tom initially has, which is 15.
Next, I note that his dad gave him an additional 33 dimes.
To find the total number of dimes Tom has now, I add the original number of dimes to the number of dimes his dad gave him.
So, 15 (original dimes) plus 33 (additional dimes) equals... | 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? | orca_math | 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. | null | null | <think>
First, I identify the number of dimes Tom initially has, which is 15.
Next, I note that his dad gave him an additional 33 dimes.
To find the total number of dimes Tom has now, I add the original number of dimes to the number of dimes his dad gave him.
So, 15 (original dimes) plus 33 (additional dimes) equals... | 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. | 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 | R1-Distill-SFT | 1 | |
id_16 | <think>
First, determine the number of dolls in the big boxes by multiplying the number of big boxes by the number of dolls each big box contains.
Next, determine the number of dolls in the small boxes by multiplying the number of small boxes by the number of dolls each small box contains.
Finally, add the number of ... | 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? | orca_math | 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
Now, we add the number of dolls from ... | null | null | <think>
First, determine the number of dolls in the big boxes by multiplying the number of big boxes by the number of dolls each big box contains.
Next, determine the number of dolls in the small boxes by multiplying the number of small boxes by the number of dolls each small box contains.
Finally, add the number of ... | 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
Now, we add the number of dolls from ... | 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
Now, we add the number of dolls from ... | 71 | R1-Distill-SFT | 1 | |
id_17 | <think>
First, I need to determine the total weight of the saltwater solution by adding the weight of the salt to the weight of the water.
Next, I will calculate the fraction of the total weight that the salt represents by dividing the weight of the salt by the total weight of the solution.
Finally, I will simplify t... | Put 6 kg of salt into 30 kg of water. The weight of the salt accounts for what fraction of the total weight of the saltwater solution?
A: $\boxed{\frac{1}{5}}$
B: $\boxed{\frac{1}{6}}$
C: $\boxed{\frac{1}{30}}$
D: | cn_k12 | Calculate as follows: $6 \div (30+6)$
$= 6 \div 36$
$= \boxed{\frac{1}{6}}$
Thus, the weight of the salt accounts for $\boxed{\frac{1}{6}}$ of the total weight of the saltwater solution.
Therefore, the correct answer is: B. | null | null | <think>
First, I need to determine the total weight of the saltwater solution by adding the weight of the salt to the weight of the water.
Next, I will calculate the fraction of the total weight that the salt represents by dividing the weight of the salt by the total weight of the solution.
Finally, I will simplify t... | Put 6 kg of salt into 30 kg of water. The weight of the salt accounts for what fraction of the total weight of the saltwater solution?
A: $\boxed{\frac{1}{5}}$
B: $\boxed{\frac{1}{6}}$
C: $\boxed{\frac{1}{30}}$
D: | Calculate as follows: $6 \div (30+6)$
$= 6 \div 36$
$= \boxed{\frac{1}{6}}$
Thus, the weight of the salt accounts for $\boxed{\frac{1}{6}}$ of the total weight of the saltwater solution.
Therefore, the correct answer is: B. | Calculate as follows: $6 \div (30+6)$
$= 6 \div 36$
$= \boxed{\frac{1}{6}}$
Thus, the weight of the salt accounts for $\boxed{\frac{1}{6}}$ of the total weight of the saltwater solution.
Therefore, the correct answer is: B. | \frac{1 | R1-Distill-SFT | 1 | |
id_18 | <think>
To determine the measure of angle \( G \), we start by noting that angle \( C \) is \( 120^\circ \) and forms a linear pair with angle \( D \). Since linear pairs add up to \( 180^\circ \), we can find angle \( D \) as follows:
\[
D = 180^\circ - 120^\circ = 60^\circ
\]
Next, we consider the triangle containi... | In a geometric configuration, angle $C$ measures $120^\circ$ and forms a linear pair with angle $D$. In an adjacent triangle, angle $E$ measures $50^\circ$ and angle $F$ is congruent to angle $D$. Determine the measure of angle $G$, the third angle in the triangle containing angles $E$ and $F$.
$\text{(A)}\ 50^\circ \q... | synthetic_amc | 1. **Calculate angle $D$**: Since angle $D$ forms a linear pair with $120^\circ$ angle $C$, we have:
\[
D = 180^\circ - 120^\circ = 60^\circ.
\]
2. **Analyze the triangle with angles $E, F, G$**: Angle $E$ is given as $50^\circ$ and angle $F$ is congruent to angle $D$, so $F = 60^\circ$.
3. **Calculate angle... | null | null | <think>
To determine the measure of angle \( G \), we start by noting that angle \( C \) is \( 120^\circ \) and forms a linear pair with angle \( D \). Since linear pairs add up to \( 180^\circ \), we can find angle \( D \) as follows:
\[
D = 180^\circ - 120^\circ = 60^\circ
\]
Next, we consider the triangle containi... | In a geometric configuration, angle $C$ measures $120^\circ$ and forms a linear pair with angle $D$. In an adjacent triangle, angle $E$ measures $50^\circ$ and angle $F$ is congruent to angle $D$. Determine the measure of angle $G$, the third angle in the triangle containing angles $E$ and $F$.
$\text{(A)}\ 50^\circ \q... | 1. **Calculate angle $D$**: Since angle $D$ forms a linear pair with $120^\circ$ angle $C$, we have:
\[
D = 180^\circ - 120^\circ = 60^\circ.
\]
2. **Analyze the triangle with angles $E, F, G$**: Angle $E$ is given as $50^\circ$ and angle $F$ is congruent to angle $D$, so $F = 60^\circ$.
3. **Calculate angle... | 1. **Calculate angle $D$**: Since angle $D$ forms a linear pair with $120^\circ$ angle $C$, we have:
\[
D = 180^\circ - 120^\circ = 60^\circ.
\]
2. **Analyze the triangle with angles $E, F, G$**: Angle $E$ is given as $50^\circ$ and angle $F$ is congruent to angle $D$, so $F = 60^\circ$.
3. **Calculate angle... | C | R1-Distill-SFT | 1 | |
id_19 | <think>
First, I need to determine how many boxes Jungkook requires to store all 10 balls, with each box holding 5 balls.
To find the number of boxes, I can divide the total number of balls by the number of balls each box can hold.
So, 10 balls divided by 5 balls per box equals 2 boxes.
Therefore, Jungkook needs 2 b... | There are 10 balls. Jungkook wants to put 5 balls in one box. How many boxes does he need at this time? | orca_math |
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. | null | null | <think>
First, I need to determine how many boxes Jungkook requires to store all 10 balls, with each box holding 5 balls.
To find the number of boxes, I can divide the total number of balls by the number of balls each box can hold.
So, 10 balls divided by 5 balls per box equals 2 boxes.
Therefore, Jungkook needs 2 b... | 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. |
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 | R1-Distill-SFT | 1 | |
id_20 | <think>
First, calculate the number of correct answers Liza got by finding 90% of 60.
Next, determine Rose's correct answers by adding 2 to Liza's correct answers.
Finally, subtract the number of correct answers Rose got from the total number of items to find the number of incorrect answers.
</think>
**Solution:**
... | 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? | orca_math | 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:
60 - 56 = $\boxed{4}$ inc... | null | null | <think>
First, calculate the number of correct answers Liza got by finding 90% of 60.
Next, determine Rose's correct answers by adding 2 to Liza's correct answers.
Finally, subtract the number of correct answers Rose got from the total number of items to find the number of incorrect answers.
</think>
**Solution:**
... | 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:
60 - 56 = $\boxed{4}$ inc... | 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:
60 - 56 = $\boxed{4}$ inc... | 4 | R1-Distill-SFT | 1 | |
id_21 | <think>
First, I need to determine how much money Lilly saves in total. She saves $2 each day for 22 days.
Next, I calculate the total savings by multiplying the daily savings by the number of days:
$2/day * 22 days = $44.
Then, I find out how many flowers Lilly can buy by dividing the total savings by the cost per f... | 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? | orca_math | 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:
$44 /... | null | null | <think>
First, I need to determine how much money Lilly saves in total. She saves $2 each day for 22 days.
Next, I calculate the total savings by multiplying the daily savings by the number of days:
$2/day * 22 days = $44.
Then, I find out how many flowers Lilly can buy by dividing the total savings by the cost per f... | 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:
$44 /... | 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:
$44 /... | 11 | R1-Distill-SFT | 1 | |
id_22 | <think>
First, determine the number of pairs of shoes Anthony has by multiplying Scott's pairs by 3.
Next, find out how many pairs Jim has by subtracting 2 from Anthony's total.
Finally, calculate the difference between Anthony's and Jim's pairs of shoes to determine how many more pairs Anthony has compared to Jim.
<... | 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? | orca_math | 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. | null | null | <think>
First, determine the number of pairs of shoes Anthony has by multiplying Scott's pairs by 3.
Next, find out how many pairs Jim has by subtracting 2 from Anthony's total.
Finally, calculate the difference between Anthony's and Jim's pairs of shoes to determine how many more pairs Anthony has compared to Jim.
<... | 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. | 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 | R1-Distill-SFT | 1 | |
id_23 | <think>
First, I need to determine how many DS games Katie's friends have. I know that Katie has a total of 81 DS games and that she has 22 more games than her friends.
To find out how many games her friends have, I can set up an equation where the number of games her friends have is represented by \( F \).
According... | 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? | orca_math | 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... | null | null | <think>
First, I need to determine how many DS games Katie's friends have. I know that Katie has a total of 81 DS games and that she has 22 more games than her friends.
To find out how many games her friends have, I can set up an equation where the number of games her friends have is represented by \( F \).
According... | 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... | 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 | R1-Distill-SFT | 1 | |
id_24 | <think>
First, I need to determine the total length of fishing line John has. He buys 3 reels, each containing 100 meters of fishing line.
Next, I'll calculate the total length by multiplying the number of reels by the length of each reel:
3 reels × 100 meters per reel = 300 meters.
Now, John wants to cut this fishin... | John buys 3 reels of 100m fishing line. He cuts it into 10m sections. How many sections does he get? | gsm8k | 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... | null | null | <think>
First, I need to determine the total length of fishing line John has. He buys 3 reels, each containing 100 meters of fishing line.
Next, I'll calculate the total length by multiplying the number of reels by the length of each reel:
3 reels × 100 meters per reel = 300 meters.
Now, John wants to cut this fishin... | 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... | 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 | R1-Distill-SFT | 1 | |
id_25 | <think>
To determine the number of males in the village, we start by noting that the total population is 520 and it is divided into four equal groups. Each group is represented by a rectangle on the graph.
Since the population is divided equally, each group (rectangle) represents:
\[
\frac{520}{4} = 130
\]
Given that... | A small village has a total population of $520$. The data is shown on a graph which divides this population into four equal groups represented by rectangles. However, the labels specifying males and females are unreaded. If it is known that one rectangle represents all males in the village, how many males are there?
$\... | synthetic_amc | 1. **Understanding the Situation**: The total population is given as $520$, divided into four rectangles of equal population size. Each rectangle represents a different group (males, females, adults, children), but only the male group is needed.
2. **Formulating the Equation**: Each rectangle holds an equal quarter of... | null | null | <think>
To determine the number of males in the village, we start by noting that the total population is 520 and it is divided into four equal groups. Each group is represented by a rectangle on the graph.
Since the population is divided equally, each group (rectangle) represents:
\[
\frac{520}{4} = 130
\]
Given that... | A small village has a total population of $520$. The data is shown on a graph which divides this population into four equal groups represented by rectangles. However, the labels specifying males and females are unreaded. If it is known that one rectangle represents all males in the village, how many males are there?
$\... | 1. **Understanding the Situation**: The total population is given as $520$, divided into four rectangles of equal population size. Each rectangle represents a different group (males, females, adults, children), but only the male group is needed.
2. **Formulating the Equation**: Each rectangle holds an equal quarter of... | 1. **Understanding the Situation**: The total population is given as $520$, divided into four rectangles of equal population size. Each rectangle represents a different group (males, females, adults, children), but only the male group is needed.
2. **Formulating the Equation**: Each rectangle holds an equal quarter of... | \text{(B) | R1-Distill-SFT | 1 | |
id_26 | <think>
First, I need to determine the length of each step on the number line. Since there are nine steps from 0 to 36, I can calculate the length of each step by dividing the total distance by the number of steps.
Next, I'll use the length of each step to find the number \( x \) that is reached after taking six steps... | On a number line where the markings are equally spaced, what is the number $x$ if nine steps are taken to get from 0 to 36?
$\text{(A)}\ 20 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 28 \qquad \text{(D)}\ 32 \qquad \text{(E)}\ 36$ | synthetic_amc | 1. **Identify the total distance and the number of steps**: The problem indicates that there are nine steps from 0 to 36.
2. **Calculate the length of each step**: The total distance of 36 is divided by the number of steps (which is nine):
\[
\text{Length of each step} = \frac{36}{9} = 4
\]
3. **Determine th... | null | null | <think>
First, I need to determine the length of each step on the number line. Since there are nine steps from 0 to 36, I can calculate the length of each step by dividing the total distance by the number of steps.
Next, I'll use the length of each step to find the number \( x \) that is reached after taking six steps... | On a number line where the markings are equally spaced, what is the number $x$ if nine steps are taken to get from 0 to 36?
$\text{(A)}\ 20 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 28 \qquad \text{(D)}\ 32 \qquad \text{(E)}\ 36$ | 1. **Identify the total distance and the number of steps**: The problem indicates that there are nine steps from 0 to 36.
2. **Calculate the length of each step**: The total distance of 36 is divided by the number of steps (which is nine):
\[
\text{Length of each step} = \frac{36}{9} = 4
\]
3. **Determine th... | 1. **Identify the total distance and the number of steps**: The problem indicates that there are nine steps from 0 to 36.
2. **Calculate the length of each step**: The total distance of 36 is divided by the number of steps (which is nine):
\[
\text{Length of each step} = \frac{36}{9} = 4
\]
3. **Determine th... | B | R1-Distill-SFT | 1 | |
id_27 | <think>
First, identify the coordinates of points A and B. Point A is at (1, -1) and point B is at (1, 2).
To find the vector \(\overrightarrow{AB}\), subtract the coordinates of point A from the coordinates of point B.
Calculate the x-component of the vector:
\[
1 - 1 = 0
\]
Calculate the y-component of the vector:... | Given points A(1, -1) and B(1, 2), then $\overrightarrow{AB} = $ ______. | cn_k12 | Given A(1, -1) and B(1, 2), then $\overrightarrow{AB} = (0, 3)$.
Therefore, the answer is $(0, 3)$.
This can be directly solved using vector coordinate operations.
This question tests the coordinate operations of vectors and is a basic question.
Hence, the final answer is $\boxed{(0, 3)}$. | null | null | <think>
First, identify the coordinates of points A and B. Point A is at (1, -1) and point B is at (1, 2).
To find the vector \(\overrightarrow{AB}\), subtract the coordinates of point A from the coordinates of point B.
Calculate the x-component of the vector:
\[
1 - 1 = 0
\]
Calculate the y-component of the vector:... | Given points A(1, -1) and B(1, 2), then $\overrightarrow{AB} = $ ______. | Given A(1, -1) and B(1, 2), then $\overrightarrow{AB} = (0, 3)$.
Therefore, the answer is $(0, 3)$.
This can be directly solved using vector coordinate operations.
This question tests the coordinate operations of vectors and is a basic question.
Hence, the final answer is $\boxed{(0, 3)}$. | Given A(1, -1) and B(1, 2), then $\overrightarrow{AB} = (0, 3)$.
Therefore, the answer is $(0, 3)$.
This can be directly solved using vector coordinate operations.
This question tests the coordinate operations of vectors and is a basic question.
Hence, the final answer is $\boxed{(0, 3)}$. | (0, 3) | R1-Distill-SFT | 1 | |
id_28 | <think>
I need to determine how many bananas each of Jesse's 3 friends will receive if he shares his 21 bananas equally among them.
First, I'll identify the total number of bananas, which is 21.
Next, I'll determine the number of friends, which is 3.
To find out how many bananas each friend gets, I'll divide the tot... | Jesse has 21 bananas. If he shares them among 3 friends, each friend would get _____ bananas . | orca_math |
If Jesse shares 21 bananas among 3 friends, each friend would get 21 ÷ 3 = $\boxed{7}$ bananas. | null | null | <think>
I need to determine how many bananas each of Jesse's 3 friends will receive if he shares his 21 bananas equally among them.
First, I'll identify the total number of bananas, which is 21.
Next, I'll determine the number of friends, which is 3.
To find out how many bananas each friend gets, I'll divide the tot... | 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. |
If Jesse shares 21 bananas among 3 friends, each friend would get 21 ÷ 3 = $\boxed{7}$ bananas. | 7 | R1-Distill-SFT | 1 | |
id_29 | <think>
First, I need to understand the equation \(632 - AB1 = 41\). Here, \(AB1\) represents a three-digit number where \(A\) and \(B\) are digits.
To isolate \(AB1\), I'll subtract 41 from 632:
\[
632 - 41 = 591
\]
So, \(AB1 = 591\).
Next, I'll compare the digits of \(AB1\) with 591:
- The hundreds place: \(A = 5\)... | When 632-AB1=41, what number should go in B? | orca_math | 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... | null | null | <think>
First, I need to understand the equation \(632 - AB1 = 41\). Here, \(AB1\) represents a three-digit number where \(A\) and \(B\) are digits.
To isolate \(AB1\), I'll subtract 41 from 632:
\[
632 - 41 = 591
\]
So, \(AB1 = 591\).
Next, I'll compare the digits of \(AB1\) with 591:
- The hundreds place: \(A = 5\)... | 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... | 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 | R1-Distill-SFT | 1 | |
id_30 | <think>
First, I note that Kamari has 65 toys.
Since Anais has 30 more toys than Kamari, I add 30 to Kamari's number of toys to find out how many toys Anais has.
So, Anais has 65 + 30 = 95 toys.
To find the total number of toys altogether, I add the number of toys Kamari has to the number of toys Anais has.
Therefo... | Anais has 30 more toys than Kamari. Kamari has 65 toys in his box. How many toys are there altogether? | orca_math | 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. | null | null | <think>
First, I note that Kamari has 65 toys.
Since Anais has 30 more toys than Kamari, I add 30 to Kamari's number of toys to find out how many toys Anais has.
So, Anais has 65 + 30 = 95 toys.
To find the total number of toys altogether, I add the number of toys Kamari has to the number of toys Anais has.
Therefo... | 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. | 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 | R1-Distill-SFT | 1 | |
id_31 | <think>
First, determine the proportion of the sample relative to the total population. Since 200 students were sampled out of 1,200, the sampling ratio is 1/6.
Next, calculate the total number of female students in the school by multiplying the number of sampled females (85) by the sampling ratio (6):
F = 85 × 6 = 51... | In a health survey conducted by a certain school involving 1,200 male and female students, a stratified sampling method was used to draw a sample of 200 students. It is known that 85 females were sampled. The number of male students in the school is _______. | cn_k12 | Given that there are 1,200 students in total and that 200 students were sampled, this means that $\frac{1}{6}$ of the population was sampled because $\frac{200}{1200} = \frac{1}{6}$.
Since 85 out of the 200 sampled students are female, we can infer that the sampled females represent $\frac{1}{6}$ of all females in the... | null | null | <think>
First, determine the proportion of the sample relative to the total population. Since 200 students were sampled out of 1,200, the sampling ratio is 1/6.
Next, calculate the total number of female students in the school by multiplying the number of sampled females (85) by the sampling ratio (6):
F = 85 × 6 = 51... | In a health survey conducted by a certain school involving 1,200 male and female students, a stratified sampling method was used to draw a sample of 200 students. It is known that 85 females were sampled. The number of male students in the school is _______. | Given that there are 1,200 students in total and that 200 students were sampled, this means that $\frac{1}{6}$ of the population was sampled because $\frac{200}{1200} = \frac{1}{6}$.
Since 85 out of the 200 sampled students are female, we can infer that the sampled females represent $\frac{1}{6}$ of all females in the... | Given that there are 1,200 students in total and that 200 students were sampled, this means that $\frac{1}{6}$ of the population was sampled because $\frac{200}{1200} = \frac{1}{6}$.
Since 85 out of the 200 sampled students are female, we can infer that the sampled females represent $\frac{1}{6}$ of all females in the... | M = 690 | R1-Distill-SFT | 1 | |
id_32 | <think>
First, determine the total number of Pokémon cards Sally has after her purchase. She initially had 27 cards and bought 20 more, so she now has 47 cards.
Next, set up an equation where Sally's total cards are equal to Dan's cards plus 6, since Sally has 6 more cards than Dan. This gives the equation 47 = D + 6.... | 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? | orca_math | 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... | null | null | <think>
First, determine the total number of Pokémon cards Sally has after her purchase. She initially had 27 cards and bought 20 more, so she now has 47 cards.
Next, set up an equation where Sally's total cards are equal to Dan's cards plus 6, since Sally has 6 more cards than Dan. This gives the equation 47 = D + 6.... | 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... | 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 | R1-Distill-SFT | 1 | |
id_33 | <think>
First, determine how many oranges the boy gives to his brother by calculating one-third of 12.
Next, subtract the number of oranges given to the brother from the total to find the remainder.
Then, identify the number of oranges given to the friend, which is provided as 2.
Finally, calculate the ratio of the ... | A boy has 12 oranges. He gives one-third of this number to his brother, a fraction of the remainder to his friend, and keeps the rest for himself. His friend gets 2 oranges. What is the ratio of the number of oranges given to his friend to the remainder after giving some to his brother? | orca_math | First, let's find out how many oranges the boy gives to his brother. He gives one-third of 12 oranges to his brother, which is:
1/3 * 12 = 4 oranges
Now, let's find out how many oranges are left after giving some to his brother:
12 - 4 = 8 oranges
The boy then gives a fraction of the remaining 8 oranges to his frie... | null | null | <think>
First, determine how many oranges the boy gives to his brother by calculating one-third of 12.
Next, subtract the number of oranges given to the brother from the total to find the remainder.
Then, identify the number of oranges given to the friend, which is provided as 2.
Finally, calculate the ratio of the ... | A boy has 12 oranges. He gives one-third of this number to his brother, a fraction of the remainder to his friend, and keeps the rest for himself. His friend gets 2 oranges. What is the ratio of the number of oranges given to his friend to the remainder after giving some to his brother? | First, let's find out how many oranges the boy gives to his brother. He gives one-third of 12 oranges to his brother, which is:
1/3 * 12 = 4 oranges
Now, let's find out how many oranges are left after giving some to his brother:
12 - 4 = 8 oranges
The boy then gives a fraction of the remaining 8 oranges to his frie... | First, let's find out how many oranges the boy gives to his brother. He gives one-third of 12 oranges to his brother, which is:
1/3 * 12 = 4 oranges
Now, let's find out how many oranges are left after giving some to his brother:
12 - 4 = 8 oranges
The boy then gives a fraction of the remaining 8 oranges to his frie... | 1:4 | R1-Distill-SFT | 1 | |
id_34 | <think>
First, I need to find the value of \( g(2) \). The function \( g(x) \) is given as \( x^2 + 2 \). So, substituting \( x = 2 \) into \( g(x) \), I get:
\[ g(2) = 2^2 + 2 = 4 + 2 = 6 \]
Next, I need to find \( f(g(2)) \), which is \( f(6) \). The function \( f(x) \) is given as \( 5 - 4x \). Substituting \( x =... | If \( f(x) = 5 - 4x \) and \( g(x) = x^2 + 2 \), find \( f(g(2)) \). | synthetic_math | 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 \( \boxed{-19} \). | null | null | <think>
First, I need to find the value of \( g(2) \). The function \( g(x) \) is given as \( x^2 + 2 \). So, substituting \( x = 2 \) into \( g(x) \), I get:
\[ g(2) = 2^2 + 2 = 4 + 2 = 6 \]
Next, I need to find \( f(g(2)) \), which is \( f(6) \). The function \( f(x) \) is given as \( 5 - 4x \). Substituting \( x =... | 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 \( \boxed{-19} \). | 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 | R1-Distill-SFT | 1 | |
id_35 | <think>
First, I recognize that Eunjung is the 6th speaker from the back, which means there are 5 students behind her.
Next, there are 7 students in front of Eunjung who will give presentations.
To find the total number of students giving presentations, I add the number of students in front of Eunjung, Eunjung hersel... | 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? | orca_math | 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... | null | null | <think>
First, I recognize that Eunjung is the 6th speaker from the back, which means there are 5 students behind her.
Next, there are 7 students in front of Eunjung who will give presentations.
To find the total number of students giving presentations, I add the number of students in front of Eunjung, Eunjung hersel... | 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... | 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 | R1-Distill-SFT | 1 | |
id_36 | <think>
First, I need to determine the difference between the cash realized on selling the stock and the cash amount before brokerage. This difference will represent the amount of brokerage paid.
Next, I'll calculate the percentage of the brokerage by dividing the brokerage amount by the cash amount before brokerage a... | The cash realized on selling a 14% stock is Rs. 109.25. The cash amount before brokerage is Rs. 109. What is the percentage of the brokerage? | orca_math | To find the percentage of the brokerage, we need to calculate the difference between the cash amount before brokerage and the cash realized on selling the stock, and then find out what percentage this difference is of the cash amount before brokerage.
The difference between the cash amount before brokerage and the cas... | null | null | <think>
First, I need to determine the difference between the cash realized on selling the stock and the cash amount before brokerage. This difference will represent the amount of brokerage paid.
Next, I'll calculate the percentage of the brokerage by dividing the brokerage amount by the cash amount before brokerage a... | The cash realized on selling a 14% stock is Rs. 109.25. The cash amount before brokerage is Rs. 109. What is the percentage of the brokerage? | To find the percentage of the brokerage, we need to calculate the difference between the cash amount before brokerage and the cash realized on selling the stock, and then find out what percentage this difference is of the cash amount before brokerage.
The difference between the cash amount before brokerage and the cas... | To find the percentage of the brokerage, we need to calculate the difference between the cash amount before brokerage and the cash realized on selling the stock, and then find out what percentage this difference is of the cash amount before brokerage.
The difference between the cash amount before brokerage and the cas... | 0.23\% | R1-Distill-SFT | 1 | |
id_37 | <think>
First, I need to determine the total number of crickets desired. The user has already collected 7 crickets and needs to collect 4 more.
To find the total number of crickets needed, I add the number of crickets already collected to the number of additional crickets required.
So, 7 crickets (already collected) ... | 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? | orca_math |
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. | null | null | <think>
First, I need to determine the total number of crickets desired. The user has already collected 7 crickets and needs to collect 4 more.
To find the total number of crickets needed, I add the number of crickets already collected to the number of additional crickets required.
So, 7 crickets (already collected) ... | 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. |
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 | R1-Distill-SFT | 1 | |
id_38 | <think>
First, Ken adds jelly beans to the box until it weighs 2 pounds.
Next, he adds brownies, tripling the weight to 6 pounds.
Then, he adds another 2 pounds of jelly beans, making the total weight 8 pounds.
Finally, he adds gummy worms, doubling the weight to 16 pounds.
</think>
Let's break down the process ste... | 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... | gsm8k | 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.... | null | null | <think>
First, Ken adds jelly beans to the box until it weighs 2 pounds.
Next, he adds brownies, tripling the weight to 6 pounds.
Then, he adds another 2 pounds of jelly beans, making the total weight 8 pounds.
Finally, he adds gummy worms, doubling the weight to 16 pounds.
</think>
Let's break down the process ste... | 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.... | 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 | R1-Distill-SFT | 1 | |
id_39 | <think>
First, I need to determine the total distance Mr. Welch has already driven. He initially drove 35 miles and then drove an additional 18 miles after stopping for a pie. Adding these together gives a total of 53 miles driven so far.
Next, I will subtract the distance he has already covered from the total distanc... | 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? | orca_math | 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.
... | null | null | <think>
First, I need to determine the total distance Mr. Welch has already driven. He initially drove 35 miles and then drove an additional 18 miles after stopping for a pie. Adding these together gives a total of 53 miles driven so far.
Next, I will subtract the distance he has already covered from the total distanc... | 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.
... | 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 | R1-Distill-SFT | 1 | |
id_40 | <think>
First, determine the total number of marbles after redistribution by multiplying the number of friends by the marbles each had:
4 friends × 15 marbles each = 60 marbles.
Next, add the initial marbles of Dilan, Martha, and Veronica:
14 (Dilan) + 20 (Martha) + 7 (Veronica) = 41 marbles.
Finally, subtract the su... | 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... | orca_math | 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... | null | null | <think>
First, determine the total number of marbles after redistribution by multiplying the number of friends by the marbles each had:
4 friends × 15 marbles each = 60 marbles.
Next, add the initial marbles of Dilan, Martha, and Veronica:
14 (Dilan) + 20 (Martha) + 7 (Veronica) = 41 marbles.
Finally, subtract the su... | 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... | 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 | R1-Distill-SFT | 1 | |
id_41 | <think>
To determine the original number, let's denote it as \( x \). The problem states that when 4 is added to \( x \), the sum is completely divisible by 23. This can be expressed mathematically as:
\[
x + 4 \equiv 0 \mod 23
\]
To find \( x \), we can rearrange the equation:
\[
x \equiv -4 \mod 23
\]
Since we ar... | 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? | orca_math | 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... | null | null | <think>
To determine the original number, let's denote it as \( x \). The problem states that when 4 is added to \( x \), the sum is completely divisible by 23. This can be expressed mathematically as:
\[
x + 4 \equiv 0 \mod 23
\]
To find \( x \), we can rearrange the equation:
\[
x \equiv -4 \mod 23
\]
Since we ar... | 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... | 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 | R1-Distill-SFT | 1 | |
id_42 | <think>
To determine the imaginary part of the complex number \( z = 2 - i \), I start by recalling the standard form of a complex number, which is \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part.
In the given complex number \( z = 2 - i \), the real part is clearly \( 2 \). The imaginar... | The imaginary part of the complex number $z=2-i$ is ( )
A: 2
B: 1
C: -1
D: -i | cn_k12 | The imaginary part of the complex number $z=2-i$ is $-1$.
Therefore, the correct answer is $\boxed{C}$. | null | null | <think>
To determine the imaginary part of the complex number \( z = 2 - i \), I start by recalling the standard form of a complex number, which is \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part.
In the given complex number \( z = 2 - i \), the real part is clearly \( 2 \). The imaginar... | The imaginary part of the complex number $z=2-i$ is ( )
A: 2
B: 1
C: -1
D: -i | The imaginary part of the complex number $z=2-i$ is $-1$.
Therefore, the correct answer is $\boxed{C}$. | The imaginary part of the complex number $z=2-i$ is $-1$.
Therefore, the correct answer is $\boxed{C}$. | C | R1-Distill-SFT | 1 | |
id_43 | <think>
To determine the probability of selecting the girl from the group of candidates for the announcer position, follow these steps:
1. **Calculate the Total Number of Candidates**:
- Number of boys: 3
- Number of girls: 1
- Total candidates = 3 boys + 1 girl = 4 candidates
2. **Determine the Number of Fa... | A school is recruiting announcers for the sports day. One person will be randomly selected from three boys and one girl. The probability of selecting the girl is ( ).
A: $\frac{1}{2}$
B: $\frac{1}{3}$
C: $\frac{1}{4}$
D: $\frac{1}{5}$ | cn_k12 | To solve the problem of finding the probability of selecting the girl from the group of candidates for the announcer position, we proceed as follows:
1. **Identify the Total Number of Candidates**: There are three boys and one girl, making a total of $3 + 1 = 4$ candidates.
2. **Identify the Desired Outcome**: The de... | null | null | <think>
To determine the probability of selecting the girl from the group of candidates for the announcer position, follow these steps:
1. **Calculate the Total Number of Candidates**:
- Number of boys: 3
- Number of girls: 1
- Total candidates = 3 boys + 1 girl = 4 candidates
2. **Determine the Number of Fa... | A school is recruiting announcers for the sports day. One person will be randomly selected from three boys and one girl. The probability of selecting the girl is ( ).
A: $\frac{1}{2}$
B: $\frac{1}{3}$
C: $\frac{1}{4}$
D: $\frac{1}{5}$ | To solve the problem of finding the probability of selecting the girl from the group of candidates for the announcer position, we proceed as follows:
1. **Identify the Total Number of Candidates**: There are three boys and one girl, making a total of $3 + 1 = 4$ candidates.
2. **Identify the Desired Outcome**: The de... | To solve the problem of finding the probability of selecting the girl from the group of candidates for the announcer position, we proceed as follows:
1. **Identify the Total Number of Candidates**: There are three boys and one girl, making a total of $3 + 1 = 4$ candidates.
2. **Identify the Desired Outcome**: The de... | C | R1-Distill-SFT | 1 | |
id_44 | <think>
First, I need to calculate 80% of 45. To do this, I'll convert the percentage to a decimal by dividing by 100, which gives me 0.80. Then, I'll multiply 0.80 by 45 to find the value.
Next, I'll calculate 4/5 of 25. To simplify this, I'll divide 25 by 5 to get 5, and then multiply by 4 to find the result.
Final... | How much is 80% of 45 greater than 4/5 of 25? | orca_math | 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. | null | null | <think>
First, I need to calculate 80% of 45. To do this, I'll convert the percentage to a decimal by dividing by 100, which gives me 0.80. Then, I'll multiply 0.80 by 45 to find the value.
Next, I'll calculate 4/5 of 25. To simplify this, I'll divide 25 by 5 to get 5, and then multiply by 4 to find the result.
Final... | 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. | 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 | R1-Distill-SFT | 1 | |
id_45 | <think>
First, I need to determine the number of rooms in Heidi's apartment. Since Heidi's apartment has 3 times as many rooms as Danielle's, I multiply the number of rooms in Danielle's apartment by 3.
Next, I calculate the number of rooms in Grant's apartment. Grant's apartment has 1/9 as many rooms as Heidi's, so I... | 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? | orca_math | 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. | null | null | <think>
First, I need to determine the number of rooms in Heidi's apartment. Since Heidi's apartment has 3 times as many rooms as Danielle's, I multiply the number of rooms in Danielle's apartment by 3.
Next, I calculate the number of rooms in Grant's apartment. Grant's apartment has 1/9 as many rooms as Heidi's, so I... | 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. | 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 | R1-Distill-SFT | 1 | |
id_46 | <think>
First, I need to determine the total number of chicken wings available. The chef already had 20 chicken wings cooked and cooked an additional 25 for the group. Adding these together gives a total of 45 chicken wings.
Next, I need to divide the total number of chicken wings equally among the 5 friends. By divid... | 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? | orca_math | 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... | null | null | <think>
First, I need to determine the total number of chicken wings available. The chef already had 20 chicken wings cooked and cooked an additional 25 for the group. Adding these together gives a total of 45 chicken wings.
Next, I need to divide the total number of chicken wings equally among the 5 friends. By divid... | 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... | 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 | R1-Distill-SFT | 1 | |
id_47 | <think>
First, I need to determine the cost of one slice of cake. The problem states that a slice of cake costs three-fourths of a cup of milk tea. Given that a cup of milk tea costs $2.40, I can calculate the cost of a slice of cake by multiplying $2.40 by 3/4.
Next, I'll find the cost for two slices of cake by multi... | The cost of a slice of cake is three-fourths of the cost of a cup of milk tea. If the milk tea costs $2.40, how much do 2 slices of cake and 1 cup of milk tea cost? | gsm8k | To solve this problem, let's break it down step by step:
1. **Find the cost of a slice of cake**: Given that the cost of a slice of cake is three-fourths of the cost of a cup of milk tea, and knowing that a cup of milk tea costs $2.40, we calculate the cost of a slice of cake as follows:
\[
\text{Cost of a slice... | null | null | <think>
First, I need to determine the cost of one slice of cake. The problem states that a slice of cake costs three-fourths of a cup of milk tea. Given that a cup of milk tea costs $2.40, I can calculate the cost of a slice of cake by multiplying $2.40 by 3/4.
Next, I'll find the cost for two slices of cake by multi... | The cost of a slice of cake is three-fourths of the cost of a cup of milk tea. If the milk tea costs $2.40, how much do 2 slices of cake and 1 cup of milk tea cost? | To solve this problem, let's break it down step by step:
1. **Find the cost of a slice of cake**: Given that the cost of a slice of cake is three-fourths of the cost of a cup of milk tea, and knowing that a cup of milk tea costs $2.40, we calculate the cost of a slice of cake as follows:
\[
\text{Cost of a slice... | To solve this problem, let's break it down step by step:
1. **Find the cost of a slice of cake**: Given that the cost of a slice of cake is three-fourths of the cost of a cup of milk tea, and knowing that a cup of milk tea costs $2.40, we calculate the cost of a slice of cake as follows:
\[
\text{Cost of a slice... | \$6.00 | R1-Distill-SFT | 1 | |
id_48 | <think>
To determine the number of houses in a block, I start by noting that she receives 7 pieces of candy from each house.
She estimates receiving a total of 35 candies from each block.
To find the number of houses, I divide the total number of candies by the number of candies received per house.
This calculation ... | 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? | orca_math | 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. | null | null | <think>
To determine the number of houses in a block, I start by noting that she receives 7 pieces of candy from each house.
She estimates receiving a total of 35 candies from each block.
To find the number of houses, I divide the total number of candies by the number of candies received per house.
This calculation ... | 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. | 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 | R1-Distill-SFT | 1 |
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