Question

Rachel is waiting for her friends at the movie theater. While she is waiting, she watches two groups buy tickets and popcorn. The first group buys 5 tickets and 2 popcorns, and their total is $47.50. The second group buys 4 tickets and 1 popcorn, and their total is $35.

What system of equations could represent this situation?

a) 5x + 2y = 47.50
4x + y = 35

b) 5x + 2y = 35
4x + y = 47.50

c) 5x + y = 47.50
4x + 2y = 35

d) 5x + y = 35
4x + 2y = 47.50

Answer 1

The correct system of equations based on Rachel's observation of the groups' purchases is 5x + 2y = 47.50 for the first group, and 4x + y = 35 for the second group, where 'x' is the price of a movie ticket and 'y' is the price of popcorn.

Step-by-step explanation:

The system of equations that could represent Rachel's observation of two groups buying tickets and popcorns at the movie theater can be established using the information given about the number of tickets and popcorns each group buys, along with their respective totals. We can let 'x' represent the price of one movie ticket and 'y' represent the price of one popcorn.

According to the first group's purchase, we have the first equation: 5 tickets and 2 popcorns with a total cost of $47.50, which gives us:
5x + 2y = 47.50
And for the second group's purchase, we have the second equation: 4 tickets and 1 popcorn with a total cost of $35, which gives us:
4x + y = 35

Putting the information into a system of equations, we get the correct answer:

a) 5x + 2y = 47.50
4x + y = 35