Let x be quarters, and y be nickels.
0.25x + 0.05y = 11.50
x + y = 66
x= 66 - y
0.25(66-y)+0.05y=11.50
16.5 -0.25y+0.05y = 11.50
16.5-0.2y=11.50
-0.2y=11.50-16.5
-0.2y=-5
-0.2y/-0.22=-5/-0.2
y=25
x+y=66
x+(25)=66
x=66-25
x=41
So there are 41 quarters, and 25 nickels.