Justin and Lincoln go to the movie theater and purchase refreshments for their friends. Justin spends a total of $14.00 on 4 drinks and 4 bags of popcorn. Lincoln spends a total of $20.50 on 8 drinks and 3 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 bag of popcorn, to the nearest cent.

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