Question

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.

Answer 1

Answer: popcorn = $5.75 per bag

Explanation:

Set up the equation for each person.

Let x represent the cost of one drink and y represent the cost of one bag of popcorn.

drinks popcorn Cost EQUATION

Naomi: 9 8 $111.25 9x + 8y = 111.25

Sofia: 3 2 $33.25 3x + 2y = 33.25

Next, solve the system:

9x + 8y = 111.25 → 1(9x + 8y = 111.25) → 9x + 8y = 111.25

3x + 2y = 33.25 → -3(3x + 2y = 33.25) → -9x - 6y = -99.75

2y = 11.50

y = 5.75

Answer 2

System of equations :

$111.25=$9x+$8y

$33.25=$3x+$2y

The cost of 1 drink = $x = $7.25

The cost of 1 popcorn bag = $y = $5.75

Explanation:

Given :

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.

To Find : A system of equations that can be used to find the price of one drink and the price of one bag of popcorn.

Solution :

Let cost of 1 drink = $x

⇒ cost of 9 drinks = $9x

⇒ cost of 3 drinks = $3x

Let cost of 1 popcorn bag = $y

⇒Cost of 8 popcorn bags = $8y

⇒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.

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

SOLVING A and B by using substitution method

finding value of x from equation B :

`x=(33.25-2y)/(3)`

Putting this value in Equation (A)

⇒
`111.25=9((33.25-2y)/(3))+8y`

⇒
`111.25=99.75-6y+8y`

⇒
`111.25=99.75+2y`

⇒
`y = 5.75`

Thus, cost of 1 popcorn bag =y = $5.75

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

⇒$111.25=$9x+$8(5.75)

⇒$111.25-$46 = 9x

⇒$65.25 = 9x

⇒65.25/9 = x

⇒$7.25 = x

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