Question

A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.75, how many dimes and how many quarters does he have?

Answer 1

The man has 5 dimes and 9 quarters.

Explanation:

This can either be solved by guessing and checking, or by setting up a system of equations. If `d` is the number of dimes the man has and `q` is the number of quarters, the fact that he has 14 coins means `d+q=14`. The fact that he has `$2.75=275` cents means that `10d+25q=275`.

`d+q=14\rightarrow d=14-q`

Upon substitution into the second equation, we get

`10*(14-q)+25q=275\rightarrow 140-10q+25q=275`

`\rightarrow 15q=135\rightarrow q=135/15=9`.

Therefore, `d=14-9=5`.