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?

The pile contains 17 quarters and 15 half-dollars.

Let x = the number of quarters and y = the number of half-dollars.

We have two equations:

(1) $0.25x + $0.50y = $11.75

(2) x = y + 2

Substitute the value of x from Equation (2) into Equation (1).

0.25 (y+2) + 0.50y = 11.75

0.25y + 0.50 + 0.50y = 11.75

0.75y = 11.75 - 0.50 = 11.25

y = 11.25/0.75 = 15

Substitute the value of y in Equation (2).

x = 15 + 2 = 17

The pile contains 17 quarters and 15 half-dollars.

Check: 17*$0.25 + 15*$0.50 = $4.25 + $7.50 = $11.75.