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.
