Final answer:
The total number of books in the library is 800.
Step-by-step explanation:
To find the total number of books in the library, we can set up a proportion using the given information.
Let x be the total number of fiction books.
We know that there are 3 non-fiction books for every 7 fiction books, so the ratio of non-fiction books to fiction books is 3/7.
We can write the proportion as 3/7 = 240/x.
Cross-multiplying, we get 3x = 1680.
Dividing both sides by 3, we find that x = 560.
Therefore, the total number of books in the library is 240 non-fiction books plus 560 fiction books, which is equal to 800 books.