Mary has $3.00 in nickels, dimes, and quarters. If she has twice as many dimes as quarters and twenty-seven more nickels than dimes, how many coins of each type does she have?
. Let q = number of quarters then from "she has twice as many dimes as quarters" 2q = number of dimes and from "five more nickels than dimes" 2q+5 = number of nickels . Since she has a total of $3.00: .25q + .10(2q) + .05(2q+5) = 3.00 .25q + .20q + .10q + .25 = 3.00 .55q + .25 = 3.00 .55q = 2.75 q = 2.75/.55 q = 5 (number of quarters) . number of dimes: 2q = 2(5) = 10 (number of dimes) . number of nickels: 2q+5 = 2(5)+5 = 10 + 5 = 15 (number of nickels)
