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?

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