Apiggy bank contains only quarters and nickers and there is a total of 60 coins. the total value of the coins in the bank is 7.40$. how many quarters in the piggy bank?

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

There are 22 quarters.