maggie has only dimes and quarters in her purse. she has 27 coins with a total value of 4.05. how many dimes does maggie have in her purse

d + q = 27.....q = 27 - d
0.10d + 0.25q = 4.05

0.10d + 0.25(27 - d) = 4.05
0.10d + 6.75 - 0.25d = 4.05
0.10d - 0.25d = 4.05 - 6.75
-0.15d = - 2.70
d = -2.70/ - 0.15
d = 18 <=== Maggie has 18 dimes 
and (27 - 18) = 9 quarters