Question

Dawn bought 3 video games and 9 DVDs for $75. Jerry bought

5 video games and 10 DVDs for $25 more than Dawn. How
much did each DVD cost?

Answer 1

$5

Explanation:

We can solve this using a system of linear equations. The equations are written like this:

3v + 9d = 75

5v + 10d = 100 (25 more than Dawn's total is 100)

V represents video games and d represents DVDs.

Let's isolate a variable, I'm going to isolate v in the first equation:

3v = -9d + 75

v = -3d + 25

Now that we isolated v we can plug it in to the second equation:

5(-3d + 25) + 10d = 100

-15d + 125 + 10d = 100

-5d + 125 = 100

-5d = -25

d = 5

Therefore, each DVD cost $5.

Check:

3v + 9(5) = 75

3v + 45 = 75

3v = 30

v = 10

5(10) + 10(5) = 100

50 + 50 = 100

100 = 100

I hope this helps!!

- Kay :)