Marcy has a total of 100 dimes and quarters. If the total value of the coins is $14.05, how many quarters does she have?

Let’s make two equations. D being dimes and Q being quarters.

D+Q=100

0.1d+0.25q=14.05

Now, let’s multiply the first equation by - 0.10 so that we can cancel out D.

-0.1D-0.1Q=-10

0.1d+0.25q=14.05

Let’s solve

0.15Q=4.05

Let’s divide.

Q=27

So there’s 27 Quarters. Since there are 100 in total, there must be 73 dimes.

Let’s make sure this adds up.

0.25 (27) + 0.1 (73)

6.75+7.30

14.05

So there’s 27 Quarters.