Question

Aiden and Jeremiah go to the movie theater and purchase refreshments for their friends. Aiden spends a total of $46.00 on 6 drinks and 1 bag of popcorn. Jeremiah spends a total of $134.00 on 12 drinks and 8 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.

Answer 1

Answer:the cost of one drink is $7

the cost of 1 bag of popcorn is $6.5

Explanation:

Let x represent the cost of one drink.

Let y represent the cost of 1 bag of popcorn.

Aiden spends a total of $46.00 on 6 drinks and 1 bag of popcorn. This means that

6x + y = 46 - - - -- - - - - - -1

Jeremiah spends a total of $134.00 on 12 drinks and 8 bags of popcorn. This means that

12x + 8y = 134 - - - - - - - - 2

Multiplying equation 1 by 8 and equation 2 by 1, it becomes

48x + 8y = 368

12x + 8y = 134

Subtracting equation 2 from equation 1, it becomes

36x = 234

x = 234/36 = 6.5

Substituting x = 6.5 into equation 1, it becomes

6 × 6.5 + y = 46

39 + y = 46

y = 46 - 39 = 7