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?

We let x and y be the costs of each cds and dvds, respectively. Two equations may be generated through the given conditions for Sarah and Michelle.

Sarah 3x + 5y = 137

Michelle 2x + 7y = 161

Solving simultaneously for the values of x and y gives x = 14 and y = 19. Thus, each cd costs $14.

You get the following two equations:3x + 5y = 1372x + 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