Question

Kevin and Randy Muise have a jar containing 54 ​coins, all of which are either quarters or nickels. The total value of the coins in the jar is 8.30 ​$. How many of each type of coin do they​ have?

Answer 1

Kevin and Randy have 28 quarters and 54-28 = 26 nickels.

Explanation:

Let's call the number of quarters Kevin and Randy have "x".

Since all the coins in the jar are either quarters or nickels, the total number of nickels they have is 54-x.

The value of the quarters can be represented as 0.25x and the value of the nickels can be represented as 0.05(54-x).

We can set up an equation using the total value of the coins:

0.25x + 0.05(54-x) = 8.30

Expanding the second term:

0.25x + 2.7 - 0.05x = 8.30

Combining like terms:

0.20x + 2.7 = 8.30

Solving for x:

0.20x = 5.6

x = 28

So Kevin and Randy have 28 quarters and 54-28 = 26 nickels.