How many of each coin?

Question

Jack has $7.55 of change in his packet. If he has 4 more dimes than nickels, and twice as many quarters as nickels, how many of each coin does Jack have?

Answer 1

If we let: T = the total money amount ($7.55)

d = the number of dimes (need to find)

n = the number of nickles (need to find)

q = the number of quarters (need to find)

Then we can write the following expressions:

(1) d = n + 4 ---> "he has 4 more dimes than nickels"

(2) q = 2 n ---> "twice as many quarters as nickels"

(3) T = 0.10 d + 0.05 n + 0.25 q ---> the total, T, needs to be equal to the number of coins, n, d, and q, times their monetary value, 5 cents, 10 cents, and 25 cents, respectively.

Then plugging equations (1) and (2) into equation (3) we get:

T = 0.10 (n +4) + 0.05 n + 0.25 (2 n)

Plugging in T = 7.55 and simplifying (try it for yourself) gives:

n = 11

Plugging the value of n back into equations (1) and (2) allows us to solve for d and q:

d = 15 and q = 22 (again, try it for yourself!)

We can check that this is the solution by plugging back into equations (1), (2), and (3):

15 = 11 + 4

22 = 2 * 11

7.55 = 0.10 * 15 + 0.05 * 11 + 0.25 * 22

Answer 2