On Heidi's bookcase, the ratio of fiction to non-fiction books is 2 : 3 - OCR - GCSE Maths - Question 9 - 2023 - Paper 6

After removing 2 fiction books, the number of fiction books becomes:

$$2x - 2$$

The non-fiction books remain at 3x.

According to the problem, the new ratio of fiction to non-fiction books is now 5:8. This gives us the equation:

$$\frac{2x - 2}{3x} = \frac{5}{8}$$

This can be cross-multiplied to solve for x:

Cross-multiplying gives:

$$8(2x - 2) = 5(3x)$$

which simplifies to:

$$16x - 16 = 15x$$

This leads to:

$$16x - 15x = 16 \quad \Rightarrow \quad x = 16.$$

Inserting x back into the expressions for the original number of books:

• Fiction:

$$2x = 2(16) = 32$$

• Non-Fiction:

$$3x = 3(16) = 48$$

So the total original number of books was:

$$32 + 48 = 80.$$

After removing 2 fiction books, the number of fiction books is now:

$$32 - 2 = 30.$$

Thus, the total books remaining is:

$$30 + 48 = 78.$$