When working problems of this sort, it is usually convenient to let the variable represent the highest-value contributor. Here, we choose to let q represent the number of quarters. Then the number of dimes is (29 -q) and the total value is 25q +10(29 -q) = 560 . . . . . . . . . . value in cents 15q = 560 -290 q = 270/15 = 18 As we said, the number of dimes is 29 -q = 11.