# Suppose you intend to spend $60 buying books. Hardback books cost $12 and paperback cost $5. How many books of each type can you buy?

##### 1 Answer

We have two solutions:

A) All money ($60) are spent on 12 paperbacks at $5 each

B) All money ($60) are spent on 5 hardbacks at $12 each

#### Explanation:

Let's approach this as a problem with two unknown:

There is only one equation that these two variables satisfy:

Generally speaking, one equation is insufficient to find a solution for two variables among all *real* numbers. However, we should not look for *real* numbers as solutions, only for *positive integer* ones.

Since

the number of books at $12 (that is,

Therefore,

So, we have two solutions: