Kayden and Carter go to the movie theater and purchase refreshments for their friends.

Kayden spends a total of $64.50 on 3 bags of popcorn and 6 drinks.

Carter spends a total of $106.00 on 9 bags of popcorn and 8 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.

3x + 6y = 64.50equation 1

9x + 8y = 106.00equation 2

Price of a bag of popcorn is $3(300 cents) WHILE the price of one drink is $8.75(875 cents)

Step-by-step explanation:

The question here says that Kayden and Carter go to the movie theater and purchase refreshments for their friends.

Kayden spends a total of $64.50 on 3 bags of popcorn and 6 drinks.

Carter spends a total of $106.00 on 9 bags of popcorn and 8 drinks.

Now let's assume that the price of each bag of popcorn is X and the price of one drink as Y

It means that

3x + 6y = 64.50equation 1

9x + 8y = 106.00equation 2

Make "x" the subject of the formula in equation 1

3x = 64.50 - 6y

X = (64.50 - 6y)/3

Apply the above in equation 2 and we have

9[ (64.50 - 6y)/3] + 8y = 106

9(21.5 - 2y) +8y = 106

193.5 - 18y + 8y = 106

193.5 - 10y = 106

Y= (193.5 - 106)/10

Y= $8.75 (price of one drink)

Now substitute Y = 8.75 in equation 1

3x + 6y = 64.50

3x + 6(8.75) = 64.50

3X = 64.50 - 52.5

X = 12/3

X = 3

The answer for the popcorn was actually $4.00.

Step-by-step explanation:

hope this .

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