SOLUTION: At the football game, your group buys 10 hot dogs and 5 sodas and pays $12.50. Another group of people buys 7 hot dogs and 4 sodas for $9.00. What is the cost of one hot dog and

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: At the football game, your group buys 10 hot dogs and 5 sodas and pays $12.50. Another group of people buys 7 hot dogs and 4 sodas for $9.00. What is the cost of one hot dog and       Log On

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Question 157083: At the football game, your group buys 10 hot dogs and 5 sodas and pays $12.50. Another group of people buys 7 hot dogs and 4 sodas for $9.00. What is the cost of one hot dog and one soda?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Remember: Hotdog=H--> cost$(?); and Soda=S--> cost$(?)
1st group:
10H%2B5S=12.50 -----------> eqn 1
2nd group:
7H%2B4S=9.00 --------------> eqn 2
In eqn 1 we get,
H=%2812.50-5S%29%2F10 ----------> eqn 3
Substitute eqn 3 to eqn 2:
7%28%2812.50-5S%29%2F10%29%2B4S=9 --->%287%2F10%29%2812.50-5S%29%2B4S=9.00
8.75-3.5S%2B4S=9
0.5S=9-8.75
0.5S=0.25 ----> cross%280.5%29S%2Fcross%280.5%29=cross%280.25%290.50%2Fcross%280.50%29
S=0.50 --------------> cost of 1 soda=$0.50/ea
For hotdog, go eqn 3:
H=%2812.50-%285%2A0.50%29%29%2F10=%2812.50-2.50%29%2F10
H=1.00 -------> cost of 1 hotdog =$1.00/ea
In doubt? go back eqn 1:
10%281%29%2B5%280.50%29=12.50
10%2B2.50=12.50
12.50=12.50
Thank you,
Jojo