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nika2105 [10]
3 years ago
10

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 t

o 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?
Mathematics
1 answer:
slamgirl [31]3 years ago
8 0
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

<span>5x+3y=41
</span>2y=26-3x

<span>5x+3y=41
</span><span>y=13-1.5x
</span>
5x+3(13-1.5x)=41
y=13-1.5x

5x+39-4.5x=41
<span>y=13-1.5x
</span>
0.5x+39=41
<span>y=13-1.5x
</span>
0.5x=2
<span>y=13-1.5x
</span>
x=4
<span>y=13-1.5x
</span>
x=4
<span>y=7
</span>
Each box costs $4 and each program costs $7
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