Question

Brianna and Chloe go to the movie theater and purchase refreshments for their friends.

Brianna spends a total of $24.25 on 3 drinks and 4 bags of popcorn.

Chloe spends a total of $37.00 on 9 drinks and 1 bag 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

3 m + 4 n = $24.25

9 m + n = $37.00 are the required set of equations.

The cost of 1 cold drink = $3.75

The cost of 1 pop corn bag = $3.25

Explanation:

Let us assume the cost of 1 drink = $ m

And the cost of 1 bag of popcorn = $ n

Now, Brianna buys 3 drinks + 4 bag popcorn for $24.25

⇒ Cost of 3 drinks + 4 bag popcorn = $ 24.25

or, 3 ( Cost of 1 drink) + 4 ( Cost of i bag popcorn) = $ 24.25

⇒ 3 m + 4 n = $24.25 ... (1)

Also, Chloe buys 9 drinks + 1 bag popcorn for $37.00

⇒ Cost of 9 drinks + 1 bag popcorn = $37.00

or, 9 ( Cost of 1 drink) + 1 ( Cost of 1 bag popcorn) = $37.00

⇒ 9 m + n = $37.00 ... (2)

Now, solving equation (1) and (2) ,we get:

3 m + 4 n = $24.25

9 m + n = $37.00 ⇒ n = 37 - 9 m

Substitute the value of n in the equation (1),we get:

3 m + 4 n = $24.25 ⇒ 3 m + 4 ( 37 - 9 m ) = 24.25

or, 3 m + 148 - 36 m = 24.25

or, -33 m = -123.75

or, m = 123.75/33 = 3.75, or m = 3.75

Now, n = 37 - 9 m = 37 - 9(3.75) = 3.25, or n = 3.25

Hence the cost of 1 cold drink = m = $3.75

And the cost of 1 pop corn bag = n = $3.25