Rachel has five more quarters than nickels. If she has $3.65 total, how many of each coin does she have?

Let q and n represent quarters and nickels. Then q = n + 5.

$0.25q + $0.05n = $3.65 Replace n with q-5.

0.25q + 0.05 (q-5) = 3.65 Mult all terms by 100 to remove fractions.

25q + 5q - 25 = 365

Combine like terms: 30q = 390. Solve for q: q = 390/30 = 13

Rachel has 13 quarters and 13 - 5, or 8, nickels.