A collection of nickels , dimes and quarters consists of 15 coins with a value of $1.10. If the number of nickels is one less than four times the number of dimes, who many of each coin are contained in the collection?

Solution:

           N + D + Q = 15

            N = 4D - 1

             5N + 10D + 25Q = 110

               N + 2D + 5Q = 22

              N + 2D + 5(15 - N -D) = 22

               4N + 3D = 53

                4(4D-1) + 3D = 53

              D = 3 = dime

               N = 11 = nickel

               Q = 1 = quarter