Question

A high school drama club is putting on their annual theater production. There is a maximum of 800 tickets for the show. The costs of tickets are $6 before the day of the show and $9 on the day of the show. To meet the expenses of the show, the club must sell at least $5,000 worth of tickets.a) write a system of inequalities that represent this situation.b) the club sells 440 tickets before the show. Is it possible to sell enough additional tickets on the day of the show to at least meet the expenses of the show? Justify your answer.

Answer 1

a.) Let x be the number of tickets sold before the event and y the number of tickets sold on the day of the event. Then x + y =< 800 and 6x + 9y >= 5000. (b.) Suppose the club sold 440 tickets before the event, i.e. x = 440, maximum number of tickets remaining to be sold = 800 - 440 = 360. Maximum amount realized from the sales supposing all tickets were sold = 6(440) + 9(360) = 2640 + 3240 = $5880 which is greater than $5000. Therefore, it is possible for the club to sell enough additional tickets on the day of the show to meet the expenses of the show.