SOLUTION: A group of people purchased 8 hotdogs and 5 soft drinks at a cost of $16.00. A second group purchased 13 hotdogs and 6 soft drinks for a cost of $23.45. What is the cost of a sing

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Question 179908: A group of people purchased 8 hotdogs and 5 soft drinks at a cost of $16.00. A second group purchased 13 hotdogs and 6 soft drinks for a cost of $23.45. What is the cost of a single hotdog and a single soft drink?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let H be the cost of the hot dog, D be the cost of a soft drink.
1.8H%2B5D=16
2.13H%2B6D=23.45
We can use eq. 1 to get H in terms of D.
1.8H%2B5D=16
8H=16-5D
H=2-%285%2F8%29D
Now substitute this expression into eq. 2 and solve for D.
2.13H%2B6D=23.45
13%282-%285%2F8%29D%29%2B6D=23.45
26-%2865%2F8%29D%2B6D=23.45
-%2865%2F8%29D%2B%2848%2F8%29D=23.45-26
-%2817%2F8%29D=-2.55
D=%282.55%29%288%2F17%29
D=1.2
Now that you have D, go to either eq. 1 or 2 and solve for H.
H=2-%285%2F8%29D
H=2-%285%2F8%29%281.2%29
H=2-0.75
H=1.25
Hot dogs cost $1.25, soft drinks cost $1.20.