A parking meter contains dimes and quarters worth ​$9.75 . There are 66 coins in all. Find how many of each there are.

Answer 1

Let d be dimes and q be quarters

d + q= 66 (The total number of dimes and quarters is 66)

Subtract d from both sides

q = 66 - d

Since dimes are $ .10 each and quarters are $ .25 each

.10d+.25q = 9.75

Substitute q = 66 - d into equation above

.10d+.25(66 - d) = 9.75

Distribute

.10d+ 16.5 -.25d=9.75

Combine like terms

-.15d + 16.5 =9.75

Subtract 16.5 from both sides

-.15d=-6.75

Divide both sides by -.15

d=45

Since q=66-d=66-45=21

So there are 45 dimes and 21 quarters

To check

.10d+.25q = 9.75

.10(45)+.25(21)

4.50+5.25

9.75 checks