Audrey has 32 dimes and quarters in her piggy bank with a total value of $6.50. how many of the coins are dimes and how many are quarters?

D + q = 32 ... d = 32 - q

0.10d + 0.25q = 6.50

0.10 (32 - q) + 0.25q = 6.50

3.20 - 0.10q + 0.25q = 6.50

-0.10q + 0.25q = 6.50 - 3.20

0.15q = 3.30

q = 3.30 / 0.15

q = 22 < = = = 22 quarters

d + q = 32

d + 22 = 32

d = 32 - 22

d = 10 < = = = 10 dimes