Kevin and Randy Muise have a jar containing 39 coins, all of which are either quarters or nickels. The total value of the coins in the jar is \$5.95 many of each type of coin do they have? g coms, How

Question

Kevin and Randy Muise have a jar containing 39 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $5.95 how many of each type of coin do they have?

Answer 1

Hi Jessica,

Let's use the variable, n , to represent the NUMBER of nickels and the variable, q , to represent the NUMBER of quarters.

Since there is a total of 39 coins, we can write the following equation:

n + q = 39

Because each nickel is worth 5 cents and each quarter is worth 25 cents, we can write the following equation:

5n + 25q = 595

Now we can solve these two equations with two unknowns (using elimination):

n + q = 39

5n + 25q = 595

Multiply the first equation by -5 so that we can solve for q:

n + q = 39 becomes -5n - 5q = -195

Now combine this new equation with the second one:

-5n - 5q = -195

5n + 25q = 595

20q = 400

q = 20

There will be 20 quarters.

Since there is a total of 39 coins, there will be 19 nickels.

The value of these coins is indeed $5.95:

20 • $0.25 + 19 • $0.05 = $5 + 0.95 = $5.95