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A certain theater has a total of 884 seats, of which 500 are orchestra seats and the rest are balcony seats. When tickets for all the seats in the theater are sold, the total revenue from ticket sales is $34,600. What was the theater's total revenue from ticket sales for last night's performance?
(1) The price of an orchestra seat ticket is twice the price of a balcony seat ticket.
(2) For last night's performance, tickets for all the balcony seats were sold, but only 80 percent of the tickets for the orchestra seats were sold.
Please provide detailed explanations Thanks!
The number of seats for Orchestra = 500. Let the price of each ticket be x. Similarly, 384 seats for Balcony each priced at y.
We know that 500*x+384*y = 34600.
F.S 1 tells us that x = 2y. We can find out x and y, from the equation given in the Question Stem but we don't know how many seats were individually sold for orchestra and balcony. Thus not sufficient.
F.S 2 tells us that all the total no. of seats sold were 384 for balcony and 400 for orchestra. Thus, revenue for last night is 400*x+384*y. But we dont know the value of x or y. Insufficient.
Combining both F.S 1 and 2, we know the individual value of x and y and can find the net revenue of the last night's performance. Assumed that the relation b/w the cost of orchestra and balcony tickets is constant.
C.