We have two variables we are solving for. We will call them Q for the number of quarters and N for the number of nickels.
We know that the total number of coins is equal to 78, and we know that the total amount the coins are worth is equal to $13.90. With this information, we can set up a system of equations:
Q + N = 78
0.25Q + 0.05N = 13.90
Now we can solve for either Q or N in the first equation and solve by substitution by plugging the value into the second equation. Let's solve for Q:
Q = 78 - N
Now plug in 78-N for Q:
0.25(78-N) + 0.05N = 13.90
Distribute and combine like terms:
19.50 - 0.25N + 0.05N = 13.90
19.50 - 0.20N = 13.90
-0.20N = -5.60
N = 28
Now we know that there are 28 nickels. We can plug this into one of the original equations to solve for Q:
Q + 28 = 78
Q = 50
There are 50 quarters. We can verify our answer by plugging the values for A and N into the other equation (optional step to check work):
