I have $9.45 in quarters and dimes in my pocket. The number of dimes is 18 less than twice the number of quarters. How many of each coin are there?

32 dimes and 25 quarters

Explanation:

let Q = quarters and D = dimes

2Q - 18 = D

25Q + 10D = 945

we can replace D

25Q + 10 (2Q - 18) = 945

25Q + 20Q - 180 = 945

45Q = 1,125

Q = 1,125 / 45 = 25

D = (2 x 25) - 18 = 50 - 18 = 32

to check the answer:

(25 x 25) + (32 x 10) = 625 + 320 = 945