Ben and Joel are raising money for their class trip by selling wrapping paper. Ben raised $43.50 by selling 12 rolls of solid paper 9 rolls of printed paper ...

Solid paper costs 1.75 each

Printed paper costs 2.50 each

Given:

Ben = $43.50 (12 rolls solid paper and 9 rolls of printed paper)

Joel = $51.50 (8 rolls solid paper and 15 rolls of printed paper)

Let x = solid paper

Let y = printed paper

12x + 9y = 43.50

8x + 15y = 51.50

Find x:

8x + 15y = 51.50

8x = 51.50 - 15y

x = (51.50 - 15y) / 8

Substitute x:

12x + 9y = 43.50

12 (51.50 - 15y) / 8 + 9y = 43.50

(618 - 180y) / 8 + 9y = 43.50

8 (618 - 180y) / 8 + 8*9y = 43.50 * 8

618 - 180y + 72y = 348

-108y = 348 - 618

-108y = - 270

-108y/-108 = - 270/-108

y = 2.50

x = (51.50 - 15y) / 8

x = (51.50 - 15 (2.5) / 8

x = (51.50 - 37.50) / 8

x = 14/8

x = 1.75

To check: x = 1.75; y = 2.5

12x + 9y = 43.50

12 (1.75) + 9 (2.5) = 43.50

21 + 22.50 = 43.50

43.50 = 43.50

8x + 15y = 51.50

8 (1.75) + 15 (2.5) = 51.50

14 + 37.50 = 51.50

51.50 = 51.50