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.

The cost of 1 popcorn is $5.75

The cost of 1 drink is $2.25

Step-by-step 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

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step-by-step explanation: