SOLUTION: A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 5 hot dogs, 2 bags of potato chips, and 4 soft drinks for $16.50. The price of hot dogs is $2.00 mor

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Question 927444: A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 5 hot dogs, 2 bags of potato chips, and 4 soft drinks for $16.50. The price of hot dogs is $2.00 more than the price of a bag of potato chips. The cost of a soft drink is $4.25 less than the price of two hot dogs. Find the cost of each item.
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Let A = Cost of hot dogs.
Let B = Cost of potato chips
Let C = Cost of a soft drink
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Equation 1:5A+%2B+2B+%2B+4C+=+16.5 Customers order
Equation 2:A+-+2+=+B A hotdog is $2 more than a bag of chips
Equation 3: C+=+2A+-+4.25 A soft drink is $4.25 less than 2 hot dogs
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Notice that all three equations contain an "A" variable.
I wrote the equations so that they were already written in terms of A.
Now plug (A-2) into equation 1 for B. Also use (2A - 4.25) for C
Equation 1:5A+%2B+2B+%2B+4C+=+16.5
5A+%2B+2%2A%28A-2%29+%2B+4%2A%282A+-+4.25%29+=+16.5
Simplify the equation
5A+%2B+2A+-+4+%2B+8A+-+17+=+16.5
Combine like terms
15A+-+21+=+16.5
Add 21 to both sides
15A+=+37.5
Divides both sides by 15
highlight%28A+=+2.5%29
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Now plug 2.5 into equations 2 & 3 for "A" and solve.
Equation 2:A+-+2+=+B
%282.5%29+-+2+=+B
highlight_green%280.5+=+B%29
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Equation 3: C+=+2A+-+4.25
C+=+2%2A%282.5%29+-+4.25
C+=+5+-+4.25
highlight%28C+=+0.75%29