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Classroom Library Puzzle

Ms. Chen’s class is organizing their classroom library. They have a total of 48 books to arrange on shelves.

The teacher provides the following information:

There are fiction and non-fiction books.
The number of fiction books is twice the number of non-fiction books.
The books will be arranged equally on 4 shelves.
Each shelf will have both fiction and non-fiction books.
On each shelf, there will be 3 more fiction books than non-fiction books.

How many fiction and non-fiction books are on each shelf?

Justify your answer.

Solution

Let’s approach this step-by-step:

Let’s say the number of non-fiction books is x. Then the number of fiction books is 2x.
Total number of books: x + 2x = 3x = 48
Solving for x: 3x = 48, so x = 16
This means there are 16 non-fiction books and 32 fiction books.
Number of shelves: 4
Books per shelf: 48 ÷ 4 = 12
On each shelf, fiction books = non-fiction books + 3

Let’s verify:

Non-fiction books per shelf: (16 total ÷ 4 shelves) = 4
Fiction books per shelf: (32 total ÷ 4 shelves) = 8

Indeed, 8 fiction books is 3 more than 4 non-fiction books on each shelf.

Therefore, each shelf will have:

4 non-fiction books
8 fiction books

This solution satisfies all the given conditions:

Total books: 4 × 12 = 48
Fiction (32) is twice non-fiction (16)
Books are equally distributed (12 per shelf)
Each shelf has both types of books
Each shelf has 3 more fiction than non-fiction books

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