Question

At the movies, a couple bought 2 medium drinks and a large popcorn for

$8.50. At the same theater, a family bought 3 medium drinks and 2 large
popcorns for a total of $15.00. What is the cost of a medium drink?

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