The pile contains 12 nickels and 9 quarters.
Let x = the number of nickels and y = the number of quarters.
Then, we have two equations:
(1) $0.05x + $0.25y = $2.85
(2) x = y +3
Substitute the value of x from Equation (2) into Equation (1).
0.05(y+3) + 0.25y = 2.85
0.05y + 0.15 + 0.25y = 2.85
0.30y = 2.85 – 0.15 = 2.70
y = 2.70/0.30 = 9
Substitute the value of y in Equation (2).
x = 9 + 3 = 12
The pile contains 12 nickels and 9 quarters.
Check: 12×$0.05 + 9×$0.25 = $0.60 + $2.25 = $2.85.