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.