The library has a total collection of 2,630 books. The number of non-fiction books is 240 fewer than the number of fiction books but 190 more than the number of picture books. How many books of each type are there in the library?

To solve this problem, let's assign variables to represent the number of fiction books, non-fiction books, and picture books. Let F represent the number of fiction books, N represent the number of non-fiction books, and P represent the number of picture books.
We know that the total collection of books is 2630, so we can write the equation: F + N + P = 2630.
Next, we are given two pieces of information: the number of non-fiction books is 240 fewer than the number of fiction books, which can be represented as N = F - 240, and the number of non-fiction books is 190 more than the number of picture books, which can be represented as N = P + 190.
Now we can solve this system of equations to find the values of F, N, and P. Substitute the value of N in terms of F from the second equation into the first equation: F + (F - 240) + (P + 190) = 2630. Simplify the equation to get 2F + P - 50 = 2630. Rearrange the equation to isolate P: P = 2640 - 2F.
Since P represents the number of picture books, it must be a multiple of 12 (the number of books on each shelf). We can test different values of P that are multiples of 12 until we find a value that satisfies the equation. After solving the equation, we find that when P = 1320, F = 840 and N = 600.
Therefore, there are 840 fiction books, 600 non-fiction books, and 1320 picture books in the library.

Answered by Darla1012 | 2024-06-24

The library contains 840 fiction books, 600 non-fiction books, and 1190 picture books. These values were found by setting up and solving a system of equations based on the book relationships given in the problem. Each book type's quantity was calculated step-by-step to ensure accuracy.
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Answered by Darla1012 | 2024-12-24