Sarah went to an electronics store, purchased 3 CDs and 5 DVDs, and spent $137. Michelle went to the same store, bought 2 CDs and 7 DVDs, and spent $161. How much does each CD sell for at the store?

Question

anonymous · Answer

Let the price of an individual CD be "x"
and the price of an individual DVD be "y"

You get the following two equations:
3x + 5y = 137
2x + 7y = 161

If you have two equations, you can solve for two variables.

Solve for x in the first equation:

x = (137-5y)/3

Then substitute this in for "x" in the 2nd equation.

2[ (137-5y) / 3 ] + 7y = 161

Now you can solve for "y"

(274/3) - (10/3)*y + 7y = 161

(11/3)*y = 161 - (274/3)

y = 19

Now that you have "y", you can solve for "x"

2x + 7(19) = 161

x = 14

CDs cost $14 and DVDs cost $19 each