Question

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

Answer 1

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.