Question

Christian and Benjamin go to the movie theater and purchase refreshments for their friends.

Christian spends a total of $42.75 on 6 drinks and 3 bags of popcorn.

Benjamin spends a total of $98.75 on 10 drinks and 15 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

System of equations:

6d + 3p = 42.75

10d + 15p = 98.75

Drink = $5.75

Popcorn = $2.75

Explanation:

6d + 3p = 42.75

subtract 6d from both sides

3p = 42.75 - 6d

divide both sides by 3

p = 14.25 - 2d

substitute P in the second equation with the answer and solve for D

10d + 15( 14.25 - 2d) = 98.75

distribute out the 15

10d + 213.75 -30d = 98.75

-20d + 213.75 = 98.75

subtract 213.75 from both sides

-20d = -115

divide both sides by -20

d = 5.75

substitute D back in the first equation and solve for P

3p + 6(5.75) = 42.75

multiply the 6 and 5.75

3p + 34.5 = 42.75

subtract 34.5 from both sides

3p = 8.25

divide both sides by 3

p = 2.75