Question

Kevin and Randy Muise have a jar containing 63 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $13.15. How many of each type of coin do they have?
The jar contains quarters.
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Answer 1

Let’s start this off by assigning some variables. Let’s have q stand for the amount of quarters while n stands for the amount of nickels.

To start this problem, you need to utilize a system of equations. First, we know that there’s a certain number of quarters and a certain number of nickels and together there’s 63 quarters and nickels.

q + n = 63

We also know that there’s $13.15 in the jar. Since we know the value of the quarters and nickels, we can turn this into another equation.

.25q + .05n = 13.15

And there’s are two equations. Next, we have to solve for one of the variables. Either one works, but I’m going to be using q. I’m going to take the first equation since it’s easier to work with and isolate the q on one side by subtracting n from both sides.

q = 63 - n

Using that new definition for the q variable, we can substitute that into the second equation by replacing q there.

0.25(63 - n) + .05n = 13.15

Now we just need to simplify and solve for n. First we multiply both of the terms inside of the parenthesis by the .25 coefficient

15.75 - .25n + .05n = 13.15

Combine like terms

15.75 - .2n = 13.15

Add .2n to both sides to make the coefficient positive

15.75 = 13.15 + .2n

Subtract 13.15 from both sides to isolate the variable

2.60 = .2n

And finally divide both sides by .2 to solve for n.

13 = n

Now we have the amount of nickels that are in the jar. To solve for the amount of quarters is simple: Put the n value into the first equation and solve for q.

13 + q = 63

And then subtract 13 from both sides for the only step in solving for q.

q = 50.

Leaving us with a solution of 50 quarters and 13 nickels. Both of these variables can be inserted into the second equation to double check the work, but it comes out as even on both sides proving that this is the correct answer.

Hope this helped!