A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of

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A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of each coin are there?

Let d = the number of dimes and q = the number of quarters. We have two equations:
(1) d + q = 146
(2) 0.1d + 0.25q = 27.05

Rearrange (1) into (3) solving for d
(3) d = 146 - q

Substitute (3) into (2)
0.1(146 - q) + 0.25q = 27.05
14.6 - 0.1q + 0.25q = 27.05

Combine q's
0.15q + 14.6 = 27.05

Subtract 14.6 from each side
0.15q = 12.45

Divide each side by 0.15
q = 83

Plugging that into (3), we have:
d = 146 - 83
d = 63