how many of each coin is in the parking meter

Question

a parking meter contains $8.25 in dimes and quarters. if the number of quarters is 9 more than twice the number of dimes, how many of each coin is in the parking meter?

Answer 1

Here's what we know:

q = 2d + 9 (quarter count is twice dimes plus another nine)

.25q + .1d = 8.25 (total amount is $8.25)

 

we have a substitution problem here, so put in the value for q:

.25(2d + 9) + .1d = 8.25

Distribute

.5d + 2.25 + .1d = 8.25

Simplify

.6d + 2.25 = 8.25

Subtract

.6d = 6

Divide by .6

d = 10

 

q = 2 * 10 + 9

q = 20 + 9

q = 29

 

check:

.25 * 29 + .1 * 10 = 8.25

7.25 + 1 = 8.25

8.25 = 8.25