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

Answer:

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

Step-by-step 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:

$3x+9y=81.75\\3x= 81.75-9y\\x= \frac{81.75-9y}{3}$

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

$12(\frac{81.75-9y}{3})+y=47\\4(81.75-9y)+y =47\\327-36y+y=47\\327-47=35y\\y=\frac{280}{35}=8$

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

$12x+y=47\\12x+8=47\\12x=39\\x=\frac{39}{12}=3.25$

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