Mackenzie and her children went into a movie theater and she bought $99.50 worth of bags of popcorn and candies. Each bag of popcorn costs $8.50 and each candy costs $4. She bought a total of 17 bags of popcorn and candies altogether. Write a system of equations that could be used to determine the number of bags of popcorn and the number of candies that Mackenzie bought. Define the variables that you use to write the system.

Mackenzie bought 7 bags of popcorn and 10 bags of candies.

Let x represent the number of bags of popcorn and y represent the number of candies that Mackenzie bought.

She bought $99.50 worth of bags of popcorn and candies. Hence:

8.5x + 4y = 99.50    (1)

She bought a total of 17 bags of popcorn and candies altogether. Hence:

x + y = 17       (2)

Solving equations 1 and 2 simultaneously gives:

x = 7, y = 10

Therefore Mackenzie bought 7 bags of popcorn and 10 bags of candies.

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Mackenzie bought 7 bags of popcorn and 10 candies.

Step-by-step explanation:

Let x represent the number of bags of popcorn that Mackenzie bought.

Let y represent the number of candies that Mackenzie bought.

She bought a total of 17 bags of popcorn and candies altogether. This means that

x + y = 17

She bought $99.50 worth of bags of popcorn and candies. Each bag of popcorn costs $8.50 and each candy costs $4. This means that

8.5x + 4y = 99.5- - - - - - - - - - - - - - 1

Substituting x = 17 - y into equation 1, it becomes

8.5(17 - y) + 4y = 99.5

144.5 - 8.5y + 4y = 99.5

- 8.5y + 4y = 99.5 - 144.5

- 4.5y = - 45

y = - 45/ - 4.5

y = 10

x = 17 - y = 17 - 10

x = 7