Question

30 POINTS FOR WHOEVER CAN SOLVE THIS!!

A high school drama club is selling tickets for their annual musical. There is a maximum of 600 tickets for the show. The tickets cost $5 (if bought before the day of the show) and $7 (if bought on the day of the show). Let x represent the number of tickets sold before the day of the show and y represent the number of tickets sold the day of the show. To meet the expenses of the show, the club must sell at least $3500 worth of tickets. a. Write a system of inequalities that represent this situation. b. The club sells 330 tickets before the day of the show. Is it possible to sell enough additional tickets on the day of the show to meet the expenses of the show? Justify your answer.

Answer 1

The two inequalities formed will be:
One for ticket quantity:
x + y ≤ 600

One for funds generated via tickets:
5x + 7y ≥ 3500

Equating x to 330,
5(330) +7y ≥ 3500
y = 265

Checking if the other inequality holds true:
330 + 265 ≤ 600
595 ≤ 600

This inequality is still true so they can sell 265 tickets on the event day and cover their expenses.