Ashley and Grace are selling cookies and brownies at the school bake sale. Ashley sells 12 cookies and 24 brownies and makes $78. Grace sells 24 cookies and 13 brownies and makes $68.50.

Question

A. define your variables and write a system of equations to represent this scenario.

B. how much does a cookie cost? How much does a brownie cost?

Answer 1

12C + 24B = 78

24C + 13B = 68.5

multiply the 1st by 2 and subtract the 2nd to eliminate one variable

24C + 48B = 156

24C + 13B = 68.5

35B = 87.5

B = 87.5/35 = 2.5

Brownies cost $2.50

Cookies:

12C +24B = 78

12C = 78- 24(2.5) = 78 -60

C = 18/12 = $1.50 for a cookie