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.

Answer 1

1 drink costs
`\$3.25` and 1 popcorn bag cost
`\$8`

Explanation:

Given:

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

Let the price of 1 drink be x

Let the price of 1 popcorn bag be y

Sarah Spends is given by:

`12x+y =47`

Kayle spends is given by:

`3x+9y=81.75\\3x= 81.75-9y\\x= (81.75-9y)/(3)`

Now putting the value of x in sarah spending equation we get

`12((81.75-9y)/(3))+y=47\\4(81.75-9y)+y =47\\327-36y+y=47\\327-47=35y\\y=(280)/(35)=8`

Now Substituting value of y=8 in Sarah spends equation we get

`12x+y=47\\12x+8=47\\12x=39\\x=(39)/(12)=3.25`

Hence 1 drink costs
`\$3.25` and 1 popcorn bag cost
`\$8`