There are x quarters and y nickels.
The total number of coins is 60, so
x + y = 60
The total value is $7.40, so
0.25x + 0.05y = 7.4
x + y = 600.25x + 0.05y = 7.4
y = 60 - x
0.25x + 0.05y = 7.4
0.25x + 0.05(60 - x) = 7.4
0.25x + 3 - 0.05x = 7.4
0.2x + 3 = 7.4
0.2x = 4.4
x = 22
Answer: There are 22 quarters.