Question 1183781: during the movie fundraising event the concession stand at the auditorium sells popcorn, fruit,drinks. the price of a box of popcorn is 0.50 more than the price of a piece of fruit, and the price of two drinks is 0.50 less than the price of three pieces of fruit. you order two boxes of popcorn one piece of fruit and three drinks and the total comes to 7.75
a. write a system of linear equations in three variables to represent the solution . be sure to define your variables.
b. calculate the price of each item. use substitution to solve the system of three linear equations in three variables.
Found 2 solutions by robertb, MathTherapy:
Answer by robertb(5830)   (Show Source):
Answer by MathTherapy(10557)  (Show Source):
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during the movie fundraising event the concession stand at the auditorium sells popcorn, fruit,drinks. the price of a box of popcorn is 0.50 more than the price of a piece of fruit, and the price of two drinks is 0.50 less than the price of three pieces of fruit. you order two boxes of popcorn one piece of fruit and three drinks and the total comes to 7.75
a. write a system of linear equations in three variables to represent the solution . be sure to define your variables.
b. calculate the price of each item. use substitution to solve the system of three linear equations in three variables.
Let cost of a piece of fruit, a box of popcorn, and a drink, be F, P, and D, respectively
Then P = F + .5, and 2D = 3F - .5, so cost of a drink, or 
Two boxes of popcorn, 1 piece of fruit, and 3 drinks cost 7.75, so: 
6F + 3(3F - .5) = 13.5 ------- Multiplying by LCD, 2
6F + 9F - 1.5 = 13.5
15F = 15
Cost of a piece of fruit, or 
Cost of a box of popcorn, or 
Cost of a drink, or 
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