Daniela, Kieu, and Duyen decide to go to the movies one hot summer afternoon. The theater is having a summer special called Three Go Free. They will get free movie tickets if they each buy a large popcorn and a large soft drink. They take the deal and spend a total of $\$22.50$ on large popcorns and soft drinks. The next week, they go back again, only this time, they each pay $\$8.00$ for a ticket, they each get a large soft drink, but they share one large bucket of popcorn. This return trip costs them a total of $\$37.50$.

1. What is the price of a large soft drink and the price of a large bucket of popcorn?

   Hint (a):

   Set up a system of two equations to find the prices of a large popcorn and a drink.

   Answer (a):

   popcorn $=\$4.50$ and drink $=\$3.00$

2. Did you write two equations or did you use another method? If you used another method, write two equations now and solve them. If you already used a system of equations, skip this part.