word problem

Question

Carrie and Louise go to the movie theater and purchase refreshments for their friends. Carrie spends a total of $8 on one bag of popcorn and two drinks. Louise spends a total of $13.75 on two bags of popcorn and three 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.

Answer 1

p + 2d = 8

2p + 3d = 13.75

 

Well, there are a number of ways to solve this. One is to realize that Louise bought one more drink and one more popcorn for $5.75 more than Carrie, so p + d = 5.75.

 

If p + 2d = 8, then d = 8 - 5.75 = 2.25

 

p + 2.25 = 5.75

p = 3.5

 

If that doesn't jump out at you, then solve the first equation for p.

 

p = 8 - 2d

 

Because p and 8 - 2d are equal, we can substitute one for the other.

 

2(8 - 2d) + 3d = 13.75

16 - 4d + 3d = 13.75

-d = -2.25

d = 2.25

 

p = 8 - 2(2.25) 

p = 8 - 4.5

p = 3.5

 

One drink is $2.25 and one bag of popcorn is $3.50.