A Broadway theater has 400 seats, divided into orchestra main, and balcony seating. Orchestra seats sell for $70, main seats for $45, and balcony seats for $35. If all the seats are sold, the gross revenue to the theatre is $18,800. If all the main and balcony seats are sold , but only half the orchestra seats are sold, the gross revenue is $16,000. How many are there of each kind of seat.

-80 orchestra seats

-200 main seats

- 120 balcony seats

Step-by-step explanation:

Let x b number of orchestra seats

Let y be number of main seats

Let z be number of balcony seats.

Thus, we have the following equations;

For all seats sold;

70x + 45y + 35y = 18,800 - - - - eq1

For half of orchestra sold;

70•½•x + 45y + 35y = 16,000 - - eq2

For total seats;

x + y + z = 400 - - - - eq3

Solving eq1, eq2 and eq3 simultaneously, we have;

x = 80

y = 200

z = 120

Thus, we have;

-80 orchestra seats

-200 main seats

- 120 balcony seats