COIN PROBLEMS
Coin problems usually will tell you two facts:
1) the NUMBER of coins
2) the AMOUNT of value (worth) the coins
Problem: A change bank contains both nickels and quarters. The worth (value) of total coins is $7.45 and there are 33 coins totally in the bank. How many coins are nickels?
Solution: A nickel has the value of $.05 and a quarter has the value of $.25 and for the sake of ease, we will not use the $ sign in the equation.
We will use the letter N for nickels and the letter Q for quarters.
First equation involves the NUMBER of coins: N + Q = 33
Second equation involves the WORTH (VALUE) of the coin collection: .05N + .25Q = 7.45
This gives us a system of equation to solve:
N + Q = 33
.05N + .25Q = 7.45
Recall to solve a system one needs to make one of the coefficients in the problem have OPPOSITE signs. Because the top equation is easier to work with, let us decide to make the .05N have opposite signs.
N + Q = 33 multiply every term by .05 to obtain opposite signs:
.05(N)  .05(Q) = .05(33)
.05N .05Q = 1.65
Now, lets see the new, revised system:
 .05N  .05Q = 1.65
.05N + .25Q = 7.45
Now, add the equations together:
.20Q = 5.80
Now divide BOTH sides by .20
.20Q = 5.80
.20 .20
Reduce the equation: Q = 29 This means the bank has 29 quarters inside it.
Because there are 33 coins in all, we subtract to find the number of nickels.
33 – 29 = 4 There are 4 nickels in the bank.
