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"content": "A local library has a certain number of books on its shelves. If it lends out 3/5 of its books on Monday and 2/3 of the remaining books on Tuesday, it will have 140 books left. However, if it lends out 2/3 of its books on Monday and 3/5 of the remaining books on Tuesday, it will have 260 books lef... | A local library has a certain number of books on its shelves. If it lends out 3/5 of its books on Monday and 2/3 of the remaining books on Tuesday, it will have 140 books left. However, if it lends out 2/3 of its books on Monday and 3/5 of the remaining books on Tuesday, it will have 260 books left. How many books did ... | A local library has a certain number of books on its shelves. If it lends out 3/5 of its books on Monday and 2/3 of the remaining books on Tuesday, it will have 140 books left. However, if it lends out 2/3 of its books on Monday and 3/5 of the remaining books on Tuesday, it will have 260 books left. How many books did ... | ai2-adapt-dev/openmath-2-math | Let's denote the initial number of books by \( x \).
### Given:
- On Monday, the library lends out some fraction of the books.
- On Tuesday, it lends out some fraction of the remaining books.
- After these two days, certain numbers of books remain depending on the scenario.
---
### Scenario 1:
- Monday: lends out \(... | 6 | 16,578 | 0 | <think>
Okay, let's see. I need to figure out how many books the library originally had. There are two different scenarios given, each leading to a different number of remaining books. Hmm, maybe I can set up equations based on each scenario and then solve them simultaneously?
First, let me denote the initial number o... | Let \( N \) be the initial number of books in the library.
**First Scenario:**
1. On Monday, the library lends out \( \frac{3}{5} \) of its books, so the remaining books are \( \frac{2}{5}N \).
2. On Tuesday, the library lends out \( \frac{2}{3} \) of the remaining books. The remaining books after Tuesday are \( \frac... | <think>
Okay, let's see. I need to figure out how many books the library originally had. There are two different scenarios given, each leading to a different number of remaining books. Hmm, maybe I can set up equations based on each scenario and then solve them simultaneously?
First, let me denote the initial number o... | [
{
"from": "human",
"value": "A local library has a certain number of books on its shelves. If it lends out 3/5 of its books on Monday and 2/3 of the remaining books on Tuesday, it will have 140 books left. However, if it lends out 2/3 of its books on Monday and 3/5 of the remaining books on Tuesday, it will... |
[{"content":"A local library has a certain number of books on its shelves. If it lends out 3/5 of it(...TRUNCATED) | "A local library has a certain number of books on its shelves. If it lends out 3/5 of its books on M(...TRUNCATED) | "A local library has a certain number of books on its shelves. If it lends out 3/5 of its books on M(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's denote the initial number of books by \\( x \\).\n\n### Given:\n- On Monday, the library lend(...TRUNCATED) | 10 | 16,578 | 0 | "<think>\nOkay, let me try to figure out this problem. Hmm, so the library has some number of books.(...TRUNCATED) | "Let \\( B \\) be the initial number of books in the library.\n\n**First Scenario:**\n- The library (...TRUNCATED) | "<think>\nOkay, let me try to figure out this problem. Hmm, so the library has some number of books.(...TRUNCATED) | [{"from":"human","value":"A local library has a certain number of books on its shelves. If it lends (...TRUNCATED) |
[{"content":"Find the radius of the circle that passes through the points $(-2,7),$ $(8,-3),$ and $((...TRUNCATED) | "Find the radius of the circle that passes through the points $(-2,7),$ $(8,-3),$ and $(4,5),$ given(...TRUNCATED) | "Find the radius of the circle that passes through the points $(-2,7),$ $(8,-3),$ and $(4,5),$ given(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n- Three points on the circle: \\( A(-2,7), B(8,-3), C(4,5) \\)\n- The center \\(O(h,k)\(...TRUNCATED) | 37 | 13,230 | 2 | "<think>\nOkay, so I need to find the radius of a circle that passes through three points: (-2,7), ((...TRUNCATED) | "Given three points \\((-2, 7)\\), \\((8, -3)\\), and \\((4, 5)\\), we need to find the radius of th(...TRUNCATED) | "<think>\nOkay, so I need to find the radius of a circle that passes through three points: (-2,7), ((...TRUNCATED) | [{"from":"human","value":"Find the radius of the circle that passes through the points $(-2,7),$ $(8(...TRUNCATED) |
[{"content":"What is the probability that a randomly selected chord of a circle will intersect a fix(...TRUNCATED) | "What is the probability that a randomly selected chord of a circle will intersect a fixed chord of (...TRUNCATED) | "What is the probability that a randomly selected chord of a circle will intersect a fixed chord of (...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem:** \nGiven a circle, a fixed chord inside the circle has length equal to the radius of t(...TRUNCATED) | 50 | 10,416 | 3 | "<think>\nOkay, so I need to figure out the probability that a randomly selected chord of a circle w(...TRUNCATED) | "To determine the probability that a randomly selected chord of a circle intersects a fixed chord of(...TRUNCATED) | "<think>\nOkay, so I need to figure out the probability that a randomly selected chord of a circle w(...TRUNCATED) | [{"from":"human","value":"What is the probability that a randomly selected chord of a circle will in(...TRUNCATED) |
[{"content":"A local library has a certain number of books on its shelves. If it lends out 3/5 of it(...TRUNCATED) | "A local library has a certain number of books on its shelves. If it lends out 3/5 of its books on M(...TRUNCATED) | "A local library has a certain number of books on its shelves. If it lends out 3/5 of its books on M(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's denote the initial number of books by \\( x \\).\n\n### Given:\n- On Monday, the library lend(...TRUNCATED) | 0 | 16,578 | 0 | "<think>\nOkay, let's see. I need to figure out how many books the library had at the beginning. The(...TRUNCATED) | "Let \\( x \\) be the initial number of books in the library.\n\n**First Scenario:**\n1. On Monday, (...TRUNCATED) | "<think>\nOkay, let's see. I need to figure out how many books the library had at the beginning. The(...TRUNCATED) | [{"from":"human","value":"A local library has a certain number of books on its shelves. If it lends (...TRUNCATED) |
[{"content":"Find all values of $b$ for which the equation\n$$x^2 + (2b+1)x + b^2 + b - 1 = 0$$\nhas(...TRUNCATED) | "Find all values of $b$ for which the equation\n$$x^2 + (2b+1)x + b^2 + b - 1 = 0$$\nhas solutions t(...TRUNCATED) | "Find all values of $b$ for which the equation\n$$x^2 + (2b+1)x + b^2 + b - 1 = 0$$\nhas solutions t(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the quadratic equation\n\\[\nx^2 + (2b+1)x + b^2 + b - 1 = 0,\n\\]\nwe want to find all value(...TRUNCATED) | 27 | 10,720 | 1 | "<think>\nAlright, let's tackle this problem. So, we need to find all values of \\( b \\) such that (...TRUNCATED) | "To find all values of \\( b \\) for which the equation\n\\[ x^2 + (2b + 1)x + b^2 + b - 1 = 0 \\]\n(...TRUNCATED) | "<think>\nAlright, let's tackle this problem. So, we need to find all values of \\( b \\) such that (...TRUNCATED) | [{"from":"human","value":"Find all values of $b$ for which the equation\n$$x^2 + (2b+1)x + b^2 + b -(...TRUNCATED) |
[{"content":"A local library has a certain number of books on its shelves. If it lends out 3/5 of it(...TRUNCATED) | "A local library has a certain number of books on its shelves. If it lends out 3/5 of its books on M(...TRUNCATED) | "A local library has a certain number of books on its shelves. If it lends out 3/5 of its books on M(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's denote the initial number of books by \\( x \\).\n\n### Given:\n- On Monday, the library lend(...TRUNCATED) | 8 | 16,578 | 0 | "<think>\nOkay, so I need to solve this library book problem. Let me read it again to make sure I un(...TRUNCATED) | "Let the initial number of books be \\( x \\).\n\n**First Scenario:**\n- On Monday, the library lend(...TRUNCATED) | "<think>\nOkay, so I need to solve this library book problem. Let me read it again to make sure I un(...TRUNCATED) | [{"from":"human","value":"A local library has a certain number of books on its shelves. If it lends (...TRUNCATED) |
[{"content":"Find all values of $b$ for which the equation\n$$x^2 + (2b+1)x + b^2 + b - 1 = 0$$\nhas(...TRUNCATED) | "Find all values of $b$ for which the equation\n$$x^2 + (2b+1)x + b^2 + b - 1 = 0$$\nhas solutions t(...TRUNCATED) | "Find all values of $b$ for which the equation\n$$x^2 + (2b+1)x + b^2 + b - 1 = 0$$\nhas solutions t(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the quadratic equation\n\\[\nx^2 + (2b+1)x + b^2 + b - 1 = 0,\n\\]\nwe want to find all value(...TRUNCATED) | 23 | 10,720 | 1 | "<think>\nOkay, so I need to find all values of \\( b \\) for which the quadratic equation \\( x^2 +(...TRUNCATED) | "To find all values of \\( b \\) for which the quadratic equation \\( x^2 + (2b + 1)x + b^2 + b - 1 (...TRUNCATED) | "<think>\nOkay, so I need to find all values of \\( b \\) for which the quadratic equation \\( x^2 +(...TRUNCATED) | [{"from":"human","value":"Find all values of $b$ for which the equation\n$$x^2 + (2b+1)x + b^2 + b -(...TRUNCATED) |
[{"content":"A local library has a certain number of books on its shelves. If it lends out 3/5 of it(...TRUNCATED) | "A local library has a certain number of books on its shelves. If it lends out 3/5 of its books on M(...TRUNCATED) | "A local library has a certain number of books on its shelves. If it lends out 3/5 of its books on M(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's denote the initial number of books by \\( x \\).\n\n### Given:\n- On Monday, the library lend(...TRUNCATED) | 2 | 16,578 | 0 | "<think>\nOkay, so I need to figure out how many books the library initially had. There are two diff(...TRUNCATED) | "Let \\( x \\) be the initial number of books in the library.\n\n**First Scenario:**\n- On Monday, t(...TRUNCATED) | "<think>\nOkay, so I need to figure out how many books the library initially had. There are two diff(...TRUNCATED) | [{"from":"human","value":"A local library has a certain number of books on its shelves. If it lends (...TRUNCATED) |
[{"content":"Find all values of $b$ for which the equation\n$$x^2 + (2b+1)x + b^2 + b - 1 = 0$$\nhas(...TRUNCATED) | "Find all values of $b$ for which the equation\n$$x^2 + (2b+1)x + b^2 + b - 1 = 0$$\nhas solutions t(...TRUNCATED) | "Find all values of $b$ for which the equation\n$$x^2 + (2b+1)x + b^2 + b - 1 = 0$$\nhas solutions t(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the quadratic equation\n\\[\nx^2 + (2b+1)x + b^2 + b - 1 = 0,\n\\]\nwe want to find all value(...TRUNCATED) | 28 | 10,720 | 1 | "<think>\nOkay, so I have this equation: x² + (2b + 1)x + b² + b - 1 = 0, and I need to find all v(...TRUNCATED) | "To solve the problem, we need to find all values of \\( b \\) for which the quadratic equation\n\\[(...TRUNCATED) | "<think>\nOkay, so I have this equation: x² + (2b + 1)x + b² + b - 1 = 0, and I need to find all v(...TRUNCATED) | [{"from":"human","value":"Find all values of $b$ for which the equation\n$$x^2 + (2b+1)x + b^2 + b -(...TRUNCATED) |
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