If Shane has 16 quarters and nickels in his pocket, and they have a combined value of 220 cents, how many of each coin does he have?

Answer 1

Hi Isabel

To answer this, we need to come up with some equations that can keep track of all this information for us. First, let's just count the coins. There are 16 coins total. I don't know how many are quarters and how many are dimes, but I know that the number of dimes plus the number of quarters is 16. I'll use variables to tell the story:

Q+D=16

Next, let's count how much they're worth. The value of a bunch of quarters is 25 cents times however many quarters there are. The value of a bunch of dimes is 10 cents times however many dimes there are. The total value of all the coins is 220 cents:

25Q+10D=220

Now I have two equations and two unknowns, so I can solve the system of equations.

Q+D=16

25Q+10D=220

Let's start by multiplying the first equation by 10

10Q+10D=160

25Q+10D=220

Then use elimination by subtraction to get rid of 10D

15Q=60

Finally divide by 15 to find that Q is 4, so there must have been 4 quarters and 12 dimes.

Please let me know if this doesn't make sense and I can try to further clarify.