Question

Leah and Ashley go to the movie theater and purchase refreshments for their friends

Leah spends a total of 113.75 on 5 bags of popcorn and 7 drinks

Ashley spends a total of 185.50 on 6 bags of popcorn and 14 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 bag of popcorn to the nearest cent

Answer 1

The required system of equations is:

5 m+ 7 n = 113.75

6 m + 14 n = 185.50

The price of 1 bag of popcorn = $10.5

The price of 1 drink = $8.75

Explanation:

Let us assume the cost of 1 bag of popcorn = $ m

And, the cost of 1 drink = $ n

Now, Leah spends a total of 113.75 on 5 bags of popcorn and 7 drinks.

Cost of 5 bags + 7 drinks = 5 m + 7 n = $ 113.75

⇒ 5 m+ 7 n = 113.75 .. (1)

Also, Ashley spends a total of 185.50 on 6 bags of popcorn and 14 drinks

Cost of 6 bags + 14 drinks = 6 m + 14 n = $185.50

⇒ 6 m + 14 n = 185.50 .. (2)

So, here the system of equations that can be used to find the price of one bag of popcorn (m) and the price of one drink (n) are

5 m+ 7 n = 113.75 .. (1)

6 m + 14 n = 185.50 .. (2)

Now, to solve this, Multiply (1) with -2 and add with 2, we get:

-10m + 6m - 14 n + 14 n = 185.5 - 227.5

or, - 4 m = -42 , or m = 42/4 = 10.5

Putting the value of m = 10.5 in 5 m+ 7 n = 113.75 , we get n = 8.75

Hence, the price of 1 bag of popcorn = m = $10.5

And the price of 1 drink = n = $8.75