Tristan and Anthony go to the movie theater and purchase refreshments for their friends. Tristan spends a total of $132.00 on 10 drinks and 7 bags of popcorn. Anthony spends a total of $102.00 on 2 drinks and 14 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.

Question

Shirley Gross

Mathematics

14 May, 01:17

Tristan and Anthony go to the movie theater and purchase refreshments for their friends. Tristan spends a total of $132.00 on 10 drinks and 7 bags of popcorn. Anthony spends a total of $102.00 on 2 drinks and 14 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.

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Answers (1)

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Nikolas Tyler · Answer 1

Popcorn=$6

Step-by-step explanation:

1) Setting variables

d = price of drinks

p = price of popcorn

2) Writing the system of equations

10d+7p=132

2d+14p=102

3) Simplifying one equation

2d=102-14p

d=51-7p

4) Solving the other equation by plugging the first equation in

d=51-7p

10d+7p=132

10 (51-7p) + 7p=132

510-70p+7p=132

510-63p=132

63p=378

p=6

5) Substituting p=6 into the first equation

d=51-7p

d=51-42

d=9