SOLUTION: I need help with Problems Using Systems in Three Variables A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 2 hot dogs, 3 bags of potato chips, a

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I need help with Problems Using Systems in Three Variables A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 2 hot dogs, 3 bags of potato chips, a      Log On


   

Question 382379: I need help with Problems Using Systems in Three Variables
A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 2 hot dogs, 3 bags of potato
chips, and 2 soft drinks for $5.50. The price of a hot dog is $0.75 more than the price of a bag of potato chips.
The cost of a soft drink is $1.75 less than the price of two hot dogs. Find the cost of each item.
Thank you soooo Much!!! =)
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"2 hot dogs, 3 bags of potato chips, and 2 soft drinks for $5.50" ___ 2h + 3p + 2s = 550

"The price of a hot dog is $0.75 more than the price of a bag of potato chips" ___ h = p + 75 ___ h - 75 = p

"The cost of a soft drink is $1.75 less than the price of two hot dogs" ___ s = 2h - 175

you know the price of hot dogs relative to the other foods , so solve for h and use the result to find the others

substituting the equivalent values into the 1st equation ___ 2h + 3(h - 75) + 2(2h - 175) = 550

2h + 3h - 225 + 4h - 350 = 550 ___ 9h = 1125 ___ h = 125

(125) - 75 = p ___ 50 = p

s = 2(125 - 175) = 75