instruction_seed stringlengths 36 975 | response_seed stringlengths 80 10.9k | reasoning stringlengths 381 100k | deepseek_solution stringlengths 29 15.4k | __original_row_idx int64 0 34.6k | source stringclasses 1
value | final_reasoning_trace stringlengths 744 102k | conversations listlengths 2 2 |
|---|---|---|---|---|---|---|---|
Mr. Adams measures his rectangular orchard and finds it is 25 steps by X steps. Each of Mr. Adams's steps is 2 feet long. He anticipates 0.3 pounds of apples per square foot from his orchard. What is Mr. Adams's expected yield of apples? If we know the answer to the above question is 900, what is the value of unknown v... | To solve this problem, we first need to determine the area of Mr. Adams's rectangular orchard, which will allow us to calculate the expected yield of apples based on the anticipated yield per square foot.
1. **Convert the dimensions from steps to feet:**
- Width of the orchard in feet = 25 steps * 2 feet/step = ... | Okay, let's see. Mr. Adams has a rectangular orchard, and he measures it as 25 steps by X steps. Each step is 2 feet long. So, first, I need to figure out the area of the orchard in square feet because the yield is given in pounds per square foot. The expected yield is 0.3 pounds per square foot, and the answer is supp... | Mr. Adams's orchard is measured as 25 steps by \( X \) steps. Each step is 2 feet long. To find the area of the orchard in square feet, we convert the steps to feet:
- Length: \( 25 \) steps \( \times 2 \) feet/step = \( 50 \) feet
- Width: \( X \) steps \( \times 2 \) feet/step = \( 2X \) feet
The area of the orchar... | 0 | MetaMath-AIME | <think>
Okay, let's see. Mr. Adams has a rectangular orchard, and he measures it as 25 steps by X steps. Each step is 2 feet long. So, first, I need to figure out the area of the orchard in square feet because the yield is given in pounds per square foot. The expected yield is 0.3 pounds per square foot, and the answer... | [
{
"from": "human",
"value": "Mr. Adams measures his rectangular orchard and finds it is 25 steps by X steps. Each of Mr. Adams's steps is 2 feet long. He anticipates 0.3 pounds of apples per square foot from his orchard. What is Mr. Adams's expected yield of apples? If we know the answer to the above questi... |
Let u and v be the smallest positive integers such that the product of 600 with u is a perfect square and the product of 600 with v is a perfect cube. What is the sum of u and v? | To solve for the smallest positive integers \( u \) and \( v \) such that \( 600u \) is a perfect square and \( 600v \) is a perfect cube, we first need to find the prime factorization of 600.
The prime factorization of 600 is:
\[ 600 = 2^3 \times 3^1 \times 5^2 \]
### Step 1: Finding \( u \) for a perfect square... | Okay, let's see. I need to find the smallest positive integers u and v such that 600 multiplied by u is a perfect square and 600 multiplied by v is a perfect cube. Then, I have to add u and v together. Hmm, okay. I remember something about prime factorization for these kinds of problems. Let me try to recall.
First, m... | To find the smallest positive integers \( u \) and \( v \) such that \( 600u \) is a perfect square and \( 600v \) is a perfect cube, we start by factorizing 600 into its prime components:
\[
600 = 2^3 \times 3^1 \times 5^2
\]
For \( 600u \) to be a perfect square, all the exponents in the prime factorization must be... | 2 | MetaMath-AIME | <think>
Okay, let's see. I need to find the smallest positive integers u and v such that 600 multiplied by u is a perfect square and 600 multiplied by v is a perfect cube. Then, I have to add u and v together. Hmm, okay. I remember something about prime factorization for these kinds of problems. Let me try to recall.
... | [
{
"from": "human",
"value": "Let u and v be the smallest positive integers such that the product of 600 with u is a perfect square and the product of 600 with v is a perfect cube. What is the sum of u and v?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to find the smallest pos... |
Liam has 4 peaches and 8 cherries. He extracts 8 ounces of cherry juice from 4 cherries and X ounces of peach juice from 2 peaches. If he blends an equal number of peaches and cherries, what percent of the blend is cherry juice? If we know the answer to the above question is 33.33, what is the value of unknown variable... | To solve this problem, we need to determine the value of X, which represents the ounces of peach juice extracted from 2 peaches. We will also find out the percentage of cherry juice in the blend of peaches and cherries.
Let's break down the information given:
- Liam has 4 peaches and 8 cherries.
- The juice extracted ... | Alright, let's tackle this problem step by step. So, Liam has 4 peaches and 8 cherries. He makes cherry juice from 4 cherries, getting 8 ounces, and peach juice from 2 peaches, getting X ounces. Then he blends an equal number of peaches and cherries. We need to find X such that the blend is 33.33% cherry juice. Hmm, ok... | Liam has 4 peaches and 8 cherries. He extracts 8 ounces of cherry juice from 4 cherries and \( X \) ounces of peach juice from 2 peaches. We need to find \( X \) such that the blend of an equal number of peaches and cherries results in 33.33% cherry juice.
1. **Juice Extraction Details:**
- Cherry juice: 8 ounces f... | 1 | MetaMath-AIME | <think>
Alright, let's tackle this problem step by step. So, Liam has 4 peaches and 8 cherries. He makes cherry juice from 4 cherries, getting 8 ounces, and peach juice from 2 peaches, getting X ounces. Then he blends an equal number of peaches and cherries. We need to find X such that the blend is 33.33% cherry juice.... | [
{
"from": "human",
"value": "Liam has 4 peaches and 8 cherries. He extracts 8 ounces of cherry juice from 4 cherries and X ounces of peach juice from 2 peaches. If he blends an equal number of peaches and cherries, what percent of the blend is cherry juice? If we know the answer to the above question is 33.... |
At a reunion of 38 people, 18 know each other while X are strangers. There are 550 handshakes that occur at the reunion. What is the value of the unknown variable X? | To solve this problem, we need to determine the value of X, which represents the number of people who are strangers at the reunion.
Let's break down the information given:
- Total number of people at the reunion = 38
- Number of people who know each other = 18
- Therefore, number of strangers (X) = 38 - 18 = 20.
Now,... | Okay, let me try to figure out this problem. So, there's a reunion with 38 people. Out of these, 18 know each other, and X are strangers. They mention that there are 550 handshakes happening. I need to find the value of X. Hmm, let me start breaking this down step by step.
First, I remember that in problems involving ... | To solve the problem, we need to determine the number of strangers \( X \) at a reunion of 38 people where 550 handshakes occur. Here are the key steps:
1. **Total possible handshakes**: The total number of possible handshakes among 38 people is calculated using the combination formula \( \binom{38}{2} \):
\[
\b... | 3 | MetaMath-AIME | <think>
Okay, let me try to figure out this problem. So, there's a reunion with 38 people. Out of these, 18 know each other, and X are strangers. They mention that there are 550 handshakes happening. I need to find the value of X. Hmm, let me start breaking this down step by step.
First, I remember that in problems in... | [
{
"from": "human",
"value": "At a reunion of 38 people, 18 know each other while X are strangers. There are 550 handshakes that occur at the reunion. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let me try to figure out this problem. So, there's a re... |
A bag contains X green marbles and 6 red marbles. The probability that both marbles drawn are red is 15/28. What is the value of the unknown variable X? | To solve this problem, we need to calculate the probability of drawing two red marbles from a bag that contains X green marbles and 6 red marbles.
First, we need to find the total number of marbles in the bag. Since there are X green marbles and 6 red marbles, the total number of marbles is:
Total = X + 6
The proba... | Okay, so I need to figure out how many green marbles are in the bag. The problem says there are X green marbles and 6 red marbles. When you draw two marbles without replacement, the probability that both are red is 15/28. Hmm, okay. Let me remember how probability works with combinations.
First, the total number of ma... | The problem involves determining the number of green marbles, \( X \), in a bag containing \( X \) green marbles and 6 red marbles. The probability of drawing two red marbles is given as \( \frac{15}{28} \).
First, we calculate the probability of drawing two red marbles. The total number of marbles is \( X + 6 \). The... | 6 | MetaMath-AIME | <think>
Okay, so I need to figure out how many green marbles are in the bag. The problem says there are X green marbles and 6 red marbles. When you draw two marbles without replacement, the probability that both are red is 15/28. Hmm, okay. Let me remember how probability works with combinations.
First, the total numb... | [
{
"from": "human",
"value": "A bag contains X green marbles and 6 red marbles. The probability that both marbles drawn are red is 15/28. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how many green marbles are in the bag. The p... |
In a plane, if five lines are drawn such that no two lines are parallel and no three lines intersect at the same point, how many regions are created? | Let's solve this problem step by step by focusing on the number of lines added and how they divide the plane into regions.
1. **Base case**: A single line divides the plane into 2 regions.
- If there are 1 line: 2 regions.
2. **Adding a second line**: A second line that intersects the first creates 2 additiona... | Okay, so I need to figure out how many regions five lines create in a plane, given that no two lines are parallel and no three lines meet at the same point. Hmm, let me start by visualizing this. Maybe drawing a few lines and counting the regions each time. But since I can't actually draw here, I'll try to recall if th... | To determine the number of regions created by five lines in a plane, where no two lines are parallel and no three lines intersect at the same point, we use the formula for the maximum number of regions defined by \( n \) lines:
\[
R(n) = \frac{n(n + 1)}{2} + 1
\]
We start by verifying the formula with smaller values... | 5 | MetaMath-AIME | <think>
Okay, so I need to figure out how many regions five lines create in a plane, given that no two lines are parallel and no three lines meet at the same point. Hmm, let me start by visualizing this. Maybe drawing a few lines and counting the regions each time. But since I can't actually draw here, I'll try to reca... | [
{
"from": "human",
"value": "In a plane, if five lines are drawn such that no two lines are parallel and no three lines intersect at the same point, how many regions are created?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how many regions five lines create in a plane, ... |
"A circle of diameter 4 is removed from a 5 × X rectangle. The whole number closest to the area of (...TRUNCATED) | "To solve this problem, we need to determine the area of the shaded region in the rectangle after th(...TRUNCATED) | "Okay, let's see. I need to find the value of X in a 5 by X rectangle from which a circle of diamete(...TRUNCATED) | "To find the value of \\( X \\) in a \\( 5 \\times X \\) rectangle from which a circle of diameter 4(...TRUNCATED) | 4 | MetaMath-AIME | "<think>\nOkay, let's see. I need to find the value of X in a 5 by X rectangle from which a circle o(...TRUNCATED) | [{"from":"human","value":"A circle of diameter 4 is removed from a 5 × X rectangle. The whole numbe(...TRUNCATED) |
"A turtle starts from a corner of a square with side length X meters. It moves 6.4 meters along a di(...TRUNCATED) | "To solve this problem, we need to determine the location of the turtle after it has moved along the(...TRUNCATED) | "Okay, let me try to figure this problem out. So, there's a square with side length X meters. A turt(...TRUNCATED) | "The turtle starts from a corner of a square with side length \\( X \\) meters and moves 6.4 meters (...TRUNCATED) | 7 | MetaMath-AIME | "<think>\nOkay, let me try to figure this problem out. So, there's a square with side length X meter(...TRUNCATED) | [{"from":"human","value":"A turtle starts from a corner of a square with side length X meters. It mo(...TRUNCATED) |
"In a baseball game, the Red Sox and the Yankees scored a total of 62 points, with the Red Sox winni(...TRUNCATED) | "To solve this problem, we need to determine the value of X, which represents the number of points b(...TRUNCATED) | "Okay, so I need to figure out by how many points the Red Sox won against the Yankees. The total sco(...TRUNCATED) | "The total score of the game is 62 points. The Yankees scored 18 points, so the Red Sox scored:\n\n\(...TRUNCATED) | 682 | MetaMath-AIME | "<think>\nOkay, so I need to figure out by how many points the Red Sox won against the Yankees. The (...TRUNCATED) | [{"from":"human","value":"In a baseball game, the Red Sox and the Yankees scored a total of 62 point(...TRUNCATED) |
"If Olivia's car has a fuel efficiency of 35 miles per gallon and gas is priced at $4.50 per gallon,(...TRUNCATED) | "To find out how many miles Olivia can travel with a budget of $45, we can follow these steps:\n\n1.(...TRUNCATED) | "Okay, let's see. Olivia has $45 to spend on gas, and each gallon costs $4.50. Her car can go 35 mil(...TRUNCATED) | "To determine how many miles Olivia can travel with a budget of $45, we first calculate how many gal(...TRUNCATED) | 1,234 | MetaMath-AIME | "<think>\nOkay, let's see. Olivia has $45 to spend on gas, and each gallon costs $4.50. Her car can (...TRUNCATED) | [{"from":"human","value":"If Olivia's car has a fuel efficiency of 35 miles per gallon and gas is pr(...TRUNCATED) |
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