2. A high school drama club is selling tickets for their annual musical. There is a maximum of 600 tickets for the show. The tic
kets 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.
From the given scenario above, the sum of x and y should be at most 600. That is presented in the inequality, x + y ≤ 600 Then, for their income from the sales, 5x + 7y ≥ 3500 We solve the values of x and y in the system of inequalities by substituting first equal sign to both symbols, giving us with values of x and y equal to 350 and 250, respectively.
b. It is still possible for the club to sell enough additional tickets to meet their expenses. Because by selling the remaining 270 tickets for $7, they will earn $1890. Add this to (330)($5), we get an answer of $3540.
