A newspaper carrier has $7.10 in change. He has nine more quarters than dimes but three times as many nickels as quarters. How many coins of each type does he have?

Let q represent the number of quarters he has. Then q-9 is the number of dimes, and 3q is the number of nickels. His total change is ...

0.25q + 0.10 (q-9) + 0.05 (3q) = 7.10

0.50q - 0.90 = 7.10

q = (7.10 + 0.90) / 0.50 = 16

The carrier has 16 quarters, 7 dimes, and 48 nickels.