To find out, we solve the system of equations.
n + q = 52
n = -q + 52
Plug in -q + 52 for 'n' in the 2nd equation:
0.05(-q + 52) + 0.25q = 8
Distribute 0.05:
-0.05q + 2.6 + 0.25q = 8
Combine like terms:
0.2q + 2.6 = 8
Subtract 2.6 to both sides:
0.2q = 5.4
Divide 0.2 to both sides:
q = 27
Now plug this into any of the two equations to find 'n':
n + q = 52
n + 27 = 52
Subtract 27 to both sides:
n = 25
So Alexis had 27 quarters and 25 nickels.