Question

Ethan spends a total of $26.75 on 3 drinks and 5 bags of popcorn. Noah spends a total of $18.50 on 9 drinks and 2 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

$ 4.75

Explanation:

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

let x: price of drinks

let y: bags of popcorn price

SW:

3 * x + 5 * y = 26.75

9 * x + 2 * y = 18.50 => x = (18.5 - 2 * y) / 9

Replacing, we are left with that:

3 * (18.5 - 2 * y) / 9 + 5 * y = 26.75

6.167- 0.67 * y + 5 * y = 26.75

- 0.67 * y + 5 * y = 26.75 - 6.167

4.33 * y = 20,583

y = 20,583 / 4.33

y = 4.75

Now to calculate x:

x = (18.5 - 2 * 4.75) / 9

x = 1

That is, the value of the drinks is $ 1 and the value of bags of popcorn is $ 4.75