Question

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?

Answer 1

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.