A Broadway theater has 700 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $ 50 comma main seats for $ 40 comma and balcony seats for $ 25. If all the seats are sold, the gross revenue to the theater is $ 26 comma 250. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $ 22 comma 750. How many are there of each kind of seat?There are orchestra seats?
main seats?
balcony seats?

orchestra seats = 140 seats

main seats = 350 seats

balcony seats = 210 seats

Step-by-step explanation:

Let x = number of orchestra seats

Let y = number of main seats

Let z = number of balcony seats

Theater has 700 seats. Thus;

Total seat equation is;

x + y + z = 700 - - - - (1)

We are told Orchestra seats sell for $ 50, main seats for $ 40, and balcony seats for $ 25 and a gross revenue of $26,250

Thus ;

all seats revenue equation is;

50x + 40y + 25z = 26250 - - - (eq2)

Now, we are told that, when all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $ 22,750

Thus, we have;

½(50x) + 40y + 25z = 22,750

Which gives ;

25x + 40y + 25z = 22,750 ---(eq3)

Solving the 3 equations simultaneously, we have;

x = 140

y = 350

z = 210

if x = 1, then the answer is 3.5

do your own work and don"t cheat.

step-by-step explanation: