How many of each coin type does Emily have?

Question

Emily has nickels, dimes, and quarters in her collection. She has twice as many dimes as nickels and 12 fewer quarters than dimes. The total value of the coins is $9.00. How many of each coin type does Emily have?

Answer 1

We can use facts given to set up 3 equations with 3 unknowns: let n = number of nickels, d = number of dimes, q = number of quarters. (1) d = 2n; (2) q = d + 12; (3) 0.05n + 0.10d + 0.25q = 9.00. Rearrange equation 2 in terms of d:

d = q - 12. Now we have equations 1 and 2 in terms of d, so we can set them up as equal to each other:

2n = q - 12, so n = q/2 - 6. Now, substitute values of n and d in terms of q in equation 3:

0.05(q/2 - 6) + 0.1(q - 12) + 0.25q = 9.00; 0.025q - 0.3 + 0.1q - 1.2 + 0.25q = 9.00; 0.375q - 1.5 = 9.00;

0.375q = 10.50; q = 28. Equation 2:  q = 28 = d + 12, so d = 16. Equation 1: d = 2n = 16, so n = 8.

Check: 28 quarters ($7.00) plus 16 dimes ($1.60) plus 8 nickels ($0.40) adds up to $9.00