Olivia has 40 coins made up of quarters and dimes. Altogether they make $7.00. How many quarters does she have? How many dimes does she have?

Let Q be quarters and D be dimes.

We can make two equations out of the given information

Q+D=40

0.25Q+0.1D=7

we can manipulate the second equation to be:

2.5Q+D=70 (by multiplying everything by 10)

Now we subtract the first equation from this to get:

2.5Q-Q+D-D=70-40 or 1.5Q=30

Thus Q equals 20.

Since Q+D=40, 20+D=40 so D=20

Thus there are 20 Dimes, and 20 Quarters