Question

Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total of $27.50 for four bags of popcorn and two 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 and the price of a drink, to the nearest cent.

Define your variables: p = cost of 1 popcorn, d = cost of 1 drink
Write an equation for each purchase:
2p + 3d = 18.25
4p + 2d = 27.50.

Answer 1

The cost of 1 popcorn is $5.75

The cost of 1 drink is $2.25

Explanation:

Hi there!

First, let´s write the system of equations:

2p + 3d = 18.25

4p + 2d = 27.50

Now, let´s take the first equation (for example, it can be any equation) and solve it for "p":

2p + 3d = 18.25

Subtract 3d to both sides of the equation:

2p = 18.25 - 3d

divide both sides of the equation by 2:

p = (18.25 - 3d)/2

Now let´s replace p = (18.25 - 3d)/2 in the second equation and solve it for d:

4p + 2d = 27.50

4(18.25 - 3d)/2 + 2d = 27.50

2(18.25 - 3d) + 2d = 27.50

Apply distributive property:

36.5 - 6d + 2d = 27.50

subtract 36.5 to both sides of the equation:

-4d = 27.50 - 36.50

-4d = -9

divide both sides of the equation by -4:

d = -9/-4 = 2.25

The cost of 1 drink is $2.25

To calculate the price of popcorn, let´s use the equation we obtained above isolating "p":

p = (18.25 - 3d)/2

p = (18.25 - 3(2.25))/2

p = 5.75

The cost of 1 popcorn is $5.75