Question

Mike went to a football game with his family. They bought 5 boxes of popcorn and 3 programs, and spent $41. Sean's family went to the same game, bought 3 boxes of popcorn and 2 programs, and spent $26. How much does each program cost at the game? How do I solve this?

Answer 1

EZ!

Let's say each box costs $X and each program costs $Y
Thus, Mike's family spent:
$(5X+3Y)
or
$41

Sean's family spent
$(3X+2Y)
or
$26

This yields us a system of two equations:
5x+3y=41
3x+2y=26

5x+3y=41
2y=26-3x

5x+3y=41
y=13-1.5x

5x+3(13-1.5x)=41
y=13-1.5x

5x+39-4.5x=41
y=13-1.5x

0.5x+39=41
y=13-1.5x

0.5x=2
y=13-1.5x

x=4
y=13-1.5x

x=4
y=7

Each box costs $4 and each program costs $7