A pile of coins, consisting of quarters and half dollars, is worth 11.75. If there are 2 more quarte

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A pile of coins, consisting of quarters and half dollars, is worth 11.75. If there are 2 more quarters than half dollars, how many of each are there?

Let h be the number of half-dollars and q be the number of quarters. Set up two equations:
(1) q = h + 2
(2) 0.25q + 0.5h = 11.75

Substitute (1) into (2)
0.25(h + 2) + 0.5h = 11.75
0.25h + 0.5 + 0.5h = 11.75

Group h terms
0.75h + 0.5 = 11.75

Subtract 0.5 from each side
0.75h = 11.25

Divide each side by h
h = 15

Substitute h = 15 into (1)
q = 15 + 2
q = 17