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Kaylee and Olivia go to the movie theater and purchase refreshments for their friends.

Kaylee spends a total of $30.00 on 4 bags of popcorn and 12 drinks.

Olivia spends a total of $11.25 on 1 bag of popcorn and 6 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.

Respuesta :

absor201

The price of one bag of popcorn is $3.75

Step-by-step explanation:

Let,

x represent the cost of a bag of popcorn

y represent the cost of a drink.

According to given statement;

4x+12y=30      Eqn 1

x+6y=11.25      Eqn 2

Multplying Eqn 2 by 2

[tex]2(x+6y=11.25)\\2x+12y=22.50\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 1

[tex](4x+12y)-(2x+12y)=30-22.50\\4x+12y-2x-12y=7.50\\2x=7.50[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{7.50}{2}\\x=3.75[/tex]

4x+12y=30 and x+6y=11.25 can be used to find the price of one bag of popcorn and the price of one drink.

The price of one bag of popcorn is $3.75

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/11821063
  • brainly.com/question/11871074

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