## Kevin and Colton go to the movie theater and purchase refreshments for their friends. Kevin spends a total of \$45.00 on 3 drinks

Question

Kevin and Colton go to the movie theater and purchase refreshments for their friends.

Kevin spends a total of \$45.00 on 3 drinks and 2 bags of popcorn.

Colton spends a total of \$110.25 on 9 drinks and 3 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.

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1 month 2021-09-09T09:23:38+00:00 2 Answers 0

Step-by-step explanation:

x be cost of one drink

y be cost of one popcorn

Kevin:

3x + 2y = 45         ————–(i)

Colton:

9x + 3y = 110.25     ———–(ii)

Multiply (i) by (-3)

(i)*(-3)      -9x – 6y = – 135

(ii)             9x + 3y = 110.25          {Now add and so 9x will be eliminated}

– 3y = – 24.75

y = -24.75/-3

y = 8.25

Put y value in (i)

3x + 2*8.25 = 45

3x  + 16.50 = 45

3x = 45 – 16.50

3x = 28.50

x = 28.50/3

x = 9.50

Price of one drink x = \$9.50

Price of one bag of popcorn = \$8.25

\$8.25

Step-by-step explanation:

let d represent drink and p represent popcorn, then

3d + 2p = 45 → (1)

9d + 3p = 110.25 → (2)

Multiplying (1) by – 3 and adding to (2) will eliminate d, thus

– 9d – 6p = – 135 → (3)

Add (2) and (3) term by term, that is

– 3p = – 42.75 ( divide both sides by – 3 )

p = 8.25

The price of a bag of popcorn is \$8.25