Use an algebraic approach to solve the problem.

Question

Abby has 37 coins, consisting only of dimes and quarters, worth $6.55. How many dimes and how many quarters does she have?

Answer 1

number of coins (37) = dimes (d) + quarters (q)

37 = d + q --> equation 1

value of coins ($6.55) = [dimes (d) * the value of a dime ($0.1)] + [quarters (q) * the value of a quarter ($0.25)]

6.55 = 0.1d + 0.25q --> equation 2

from equation 1, d = 37 - q

use the value for d from above in equation 2

6.55 = [0.1 * (37 - q)] + 0.25q

6.55 = 3.7 - 0.1q + 0.25q

0.15q = 6.55 - 3.7 = 2.85

q = 2.85 / 0.15 = 19

d = 37 - 19 = 18

Abby has 19 quarters and 18 dimes