Question

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

Sarah spends a total of $47.00 on 12 drinks and 1 bag of popcorn.

Kaylee spends a total of $81.75 on 3 drinks and 9 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 drink, to the nearest cent.

Answer 1

Each drink costs $3.25 and each popcorn costs $8.

Explanation:

Step 1:

Assume each drink costs x dollars and each popcorn costs y dollars.

From the given data, we can write the following equations;

`12x + y = 47`, take this as equation 1,

`3x+9y=81.75`, take this as equation 2.

Step 2:

We multiply equation 2 with 4 so we can cancel out the variable x in both equations. By doing this we get

`3x+9y = 81.75`, take this as equation 3. When we subtract 3 from 1, the x variable is canceled out and y can be calculated.

`-35y = -280, y = (280)/(35) = 8`

Step 3:

Substituting this value of y in any of the previous equations we will get x's value.

Here this value of y is substituted in equation 1.

`12x+8 = 47, 12x= 39`,

`x=(39)/(12) = 3.25`

So we have x = $3.25 and y = $8. So each drink costs $3.25 and each popcorn costs $8.