Linear System Word Problem

Question

Bella and Brianna go to the movie theater and purchase refreshments for their friends.

Bella spends a total of $183.00 on 10 drinks and 12 bags of popcorn.

Brianna spends a total of $85.50 on 4 drinks and 6 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

Let D be the price of drinks and P be the price of popcorn

From the first purchase:

10D + 12P = 183

From the second purchase

4D + 6P = 85.50

You can solve these either simultaneously or by substitution. I'll show by substitution.

From the second equation

4D + 6P = 85.50

4D = 85.50 - 6P

D = 21.375 - 1.5P

We can take this value for D and plug it into the first equation:

10D + 12P = 183

10(21.375 -1.5P) = 183

213.75 - 15P +12P = 183

-3P = -30.75

P = 10.25

Now you can take this value for P and use either of the other equations to solve for D.

Answer 2