Naomi and Sofia go to the movie theater and purchase refreshments for their friends. Naomi spends a total of $111.25 on 9 drinks and 8 bags of popcorn. Sofia spends a total of $33.25 on 3 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. V

111.25=9x+8y

33.25=3x+2y

Cost of 1 popcorn bag = $5.75

Step-by-step explanation:

We are given that Naomi spends a total of $111.25 on 9 drinks and 8 bags of popcorn and Sofia spends a total of $33.25 on 3 drinks and 2 bags of popcorn.

We need to find system of equations that can be used to find the price of one drink and the price of one bag of popcorn.

Let cost of 1 drink = $x

So, cost of 9 drinks = $9x

So, cost of 3 drinks = $3x

Now, Let cost of 1 popcorn bag = $y

So, Cost of 8 popcorn bags = $8y

So, Cost of 2 popcorn bags = $2y

Since Naomi spends a total of $111.25 on 9 drinks and 8 bags of popcorn.

So, equation will be : 111.25=9x+8y - - (A)

Since, Sofia spends a total of $33.25 on 3 drinks and 2 bags of popcorn.

Thus, equation will be : 33.25=3x+2y- - (B)

We will solve A and B by using substitution method

Finding value of x from equation B:

x = (2y-33.25) / 3

Putting this value in Equation (A)

⇒111.25=9{ (2y-33.25) / 3}+8y

⇒111.25=99.75-6y+8y

⇒111.25=99.75+2y

⇒y = 5.75

Hence cost of 1 popcorn bag = y = $5.75

Now put value of y in equation A to get value of x

⇒111.25=9 x+8 (5.75)

⇒111.25-46 = 9x

⇒65.25 = 9x

⇒65.25/9 = x

⇒$7.25 = x

Hence, The cost of 1 drink = $x = $7.25