In order to find this, start by defining the number of dimes by x and the number of quarters as y. Now we can create a system of equations. Make the first about the total number of coins.
x + y = 100
Make the second about the amount of money.
.10x + .25y = 21.40
Now we can solve using elimination by multiplying the second equation by -4 and adding through.
x + y = 100
-.40x - y = -85.60
-----------------------
.60x = 14.4
x = 24
Now we can use the amount of dimes we have to find the number of quarters.
