"A collection of quarters and nickels is worth $1.95"

Question

"A collection of quarters and nickels is worth $1.95. The number of nickels is one less than 5 times the number of quarters. How many quarters and nickels are in the collection?" I need help with the question, because I do not know how to write the equation to solve it, any help would be good =)

Answer 1

Hi,

Write mathematical sentences and solve the system of equations.

 

0.25Q + 0.05N = 1.95    ...equation 1

N = 5Q -1                    ...equation 2

 

Plug equation 2 into equation 1 (for N): 

0.25Q + 0.05(5Q -1) = 1.95

0.25Q + 0.25Q -0.05 = 1.95

0.50Q - 0.05 = 1.95

0.50Q = 0.05 + 1.95

0.50Q = 2.00

      Q = 4

N = 5(4) -1

N = 19