Question

Makayla and Caroline go to the movie theater and purchase refreshments for their friends. Makayla spends a total of $49.00 on 9 bags of popcorn and 8 drinks. Caroline spends a total of $17.25 on 3 bags of popcorn and 3 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a drink, to the nearest cent.

Answer 1

The price of a bag of popcorn and a drink can be determined by setting up a system of equations based on the information given. By solving the equations, we find that the price of a drink is $2.75 to the nearest cent.

Step-by-step explanation:

To solve the question about the price of a bag of popcorn and a drink, we need to set up a system of equations based on the information given:

Makayla spends $49 on 9 bags of popcorn and 8 drinks.

Caroline spends $17.25 on 3 bags of popcorn and 3 drinks.

Let's denote the price of a bag of popcorn as p and the price of a drink as d. Using Makayla's spending, we can write the first equation as:

9p + 8d = 49

Using Caroline's spending, we can write the second equation as:

3p + 3d = 17.25

Now, we have the system of equations:

9p + 8d = 49

3p + 3d = 17.25

To solve this system, first divide the second equation by 3 to simplify:

p + d = 5.75

Next, multiply this new equation by 8 to set up for elimination with the first equation:

8p + 8d = 46

Now subtract this from the first equation:

(9p + 8d) - (8p + 8d) = 49 - 46

p = 3

Using the value of p to solve for d in the simplified second equation:

3 + d = 5.75

d = 2.75

So the price of a drink is $2.75, to the nearest cent.