Question

Makayla and Alexandra go to the movie theater and purchase refreshments for their friends.

Makayla spends a total of $70.25 on 1 bag of popcorn and 6 drinks.


Alexandra spends a total of $171.25 on 5 bags of popcorn and 12 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 drink cost $10 and Popcorn cost $10.25

Explanation:

Let B represents Pop corn

Let D represents Drinks

We create our equation as

1B + 6D= 70.25..........Equ i

5b + 12D =171.25.......Equ ii

Kindly check attached picture for the workings

Answer 2

Drinks cost $10 and bag of popcorn $10.25

Explanation:

In this case we can solve it using a 2x2 system of equations, like this:

let x: price of bag of popcorn

let y: price of drinks

So:

1 * x + 6 * y = 70.25 => x = 70.25 - 6 * y

5 * x + 12 * y = 171.25

Replacing, we are left with that:

5 * (70.25 - 6 * y) + 12 * y = 171.25

351.25 - 30 * y + 12 * y = 171.25

- 30 * y + 12 * y = 171.25 - 351.25

-18 * y = -180

y = 180/18

y = 10

Now to calculate x:

x = 70.25 - 6 * 10

x = 10.25

this means that the drinks cost $10 and bag of popcorn $10.25