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?

2.75=.25Q+.1D; Q+D=14 . Q=14-D by eq. 2. 2.75=.25(14-D)+.1D by eq .1. 2.75=3.5-.15D; -.75=-.15D; D=5. Thus we need 2.25 worth of quarters, or 9 quarters. We have 5 dimes and 9 quarters