Myah has a coin purse that is filled with 24 dimes and quarters. She has $3.60 in all. How many dimes are there? Use the method of substitution to solve.

Maya has 24 dimes (d) and quarters (q), and they add up to $3.60. From that I know these two things:
d + q = 24
Some amount of dimes and quarters adds up to 24 total coins
0.1d + 0.25q = 3.60
Some amount of 10 cent coins and 25 cent coins add to 3.60 dollars

To solve with substitution, I first want to get one variable alone on a side. I am going to do this with the first equation.
d + q = 24
q = 24 - d

Now that I know what q equals, I can substitute 24 - d in for q in the second equation.
0.1d + 0.25q = 3.60
0.1d + 0.25(24-d) =3.60

I can now solve for d:
0.1d + 0.25(24-d) =3.60
0.1d + 6 - 0.25d = 3.60
-0.15d + 6 = 3.60
0.15d = -2.4
d = 16

Now i know that there are 16 dimes. I can now substitue 16 in for d in the first equation to solve for q.

d + q = 24
16 + q =24
q = 8

There are 16 dimes and 8 quarters. To double check, you can plug in your answer for the variables in the original equations and make sure both sides equal each other

The correct answer is 7