Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.

Question

• Jacob and Zachary go to the movie theatre 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.

Answer 1

let's make p stand for popcorn and d for drinks. Using those variables, we can create our equations:

2p + 3d = 18.25

4p + 2d = 27.50

 

From this, we can use substitution or elimination to solve:

For substitution, in the second equations, we could factor out a 2, divide both sides by 2, and then move the left over 2p to the other side to isolate d to put into the first equation.

For elimination, we can multiply the first equation by -2 so that we can remove the 4p and focus on solving for d.

 

I'll be using elimination in this case:

-2(2p + 3d = 18.25) --> -4p - 6d = -36.50

 

-4p - 6d = -36.50

4p  + 2d = 27.50

-4d = -9.00

d = 2.25

 

4p + 2 * 2.25 = 27.50

4p + 4.50 = 27.50

4p = 23.00

p = 5.75

 

Now let's check our answer:

2 * 5.75 + 3 * 2.25 = 18.25

11.50 + 6.75 = 18.25

18.25 = 18.25

 

So drinks cost $2.25 and popcorn $5.75