Books and budget

Statement

I have $150$ euros. Each book costs $18$ euros and I want to keep at least $20$ euros for dinner. At most how many books can I buy?

Solution

Let $n$ be the number of books. The spending $18n$ must leave at least $20$ euros: $18n \le 150 - 20 = 130 \implies n \le \frac{130}{18} = 7.22\ldots$ Since $n$ is an integer, the maximum is $n = 7$. Check: with $7$ books I spend $126$ euros and $24 \ge 20$ remain; with $8$ books I would spend $144$ euros and only $6 < 20$ would remain. Correct. $\boxed{7 \text{ books}}$