When Cullen cleaned behind his dresser, he found 73 cents, all in nickels and pennies. There were 25 coins. How many were nickels?

Let n = number of nickels, and p = number of pennies.

The number of coins is 25, so we get this equation.

n + p = 25

The value of the coins is 0.05 per nickel, and 0.01 per penny.

0.05n + 0.01p = 0.73

Now you have a system of equations.

n + p = 25

0.05n + 0.01p = 0.73

Solve the first equation for n:

n = 25 - p

Now substitute into the second equation.

0.05 (25 - p) + 0.01p = 0.73

1.25 - 0.05p + 0.01p = 0.73

-0.04p = - 0.52

p = 13

There were 13 pennies.

Now we substitute 13 for p in n + p = 25 to find out the number of nickels.

n + 13 = 25

n = 12

There are 13 pennies and 12 nickels.

Check: 13 pennies and 12 nickels does total 25 coins.

13 * 0.01 + 12 * 0.05 = 0.13 + 0.60 = 0.73

The value is $0.73.

Our answer is correct.