Question

A Dinner Theatre actress is paid $250 per day to rehearse the play and $500 per day to perform in front of an audience. In one season, an actress earned between $2000 and $5000. Write a system of inequalities that represents this situation.

a) 250x + 500y ≤ 2000 and 250x + 500y ≥ 5000
b) 250x + 500y ≥ 2000 and 250x + 500y ≤ 5000
c) 250x + 500y ≥ 2000 and 250x + 500y ≤ 5000
d) 250x + 500y ≤ 2000 and 250x + 500y ≥ 5000

Answer 1

The correct system of inequalities for the actress's salary situation is 250x + 500y ≥ 2000 and 250x + 500y ≤ 5000.

Step-by-step explanation:

In the scenario where a Dinner Theatre actress is paid $250 per day to rehearse and $500 per day to perform, and her earnings for one season are between $2000 and $5000, we are to write a system of inequalities to represent this situation. The correct system of inequalities would account for the number of rehearsal days (x) and performance days (y). Thus, given that the actress should earn at least $2000 but no more than $5000, our inequalities would look like this:

• 250x + 500y ≥ 2000 (The actress earns at least $2000)
• 250x + 500y ≤ 5000 (The actress earns no more than $5000)

Therefore, the correct answer is option (c): 250x + 500y ≥ 2000 and 250x + 500y ≤ 5000.