daniela, kieu, and duyen decide to go to the movies one hot summer afternoon. the theater is having a summer…

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 $22.50 on large popcorns and soft drinks. the next week, they go back again, only this time, they each pay $8.00 for their 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. (a) find the price of a large soft drink and the price of a large bucket of popcorn. (b) 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.

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 $22.50 on large popcorns and soft drinks. the next week, they go back again, only this time, they each pay $8.00 for their 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. (a) find the price of a large soft drink and the price of a large bucket of popcorn. (b) 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.

Answer

Explanation:

Step1: Set up equations

Let (x) be the price of a large soft - drink and (y) be the price of a large bucket of popcorn. First trip: (3x + 3y=22.5) (divide by 3) (\Rightarrow x + y = 7.5) (\Rightarrow y=7.5 - x) Second trip: (3\times8+3x + y=37.5) (\Rightarrow24+3x + y=37.5) (\Rightarrow3x + y=13.5)

Step2: Substitute (y = 7.5 - x) into (3x + y=13.5)

(3x+(7.5 - x)=13.5) (3x + 7.5-x=13.5) (2x=13.5 - 7.5) (2x = 6) (x = 3)

Step3: Find (y)

Substitute (x = 3) into (y=7.5 - x) (y=7.5-3) (y = 4.5)

Answer:

The price of a large soft - drink is ($3) and the price of a large bucket of popcorn is ($4.5)