A Broadway theater has 800 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $ 40 comma main seats for $ 30 comma and balcony seats for $ 20.  If all the seats are sold, the gross revenue to the theater is $ 23 comma 200.  If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $ 20 comma 000. How many are there of each kind of seat? orchestra seats: main seats: balcony seats:

orchestra seats: main seats: balcony seats: 160: 400: 240

Step-by-step explanation:

Let number of orchestra seats = x

Let number of main seats = y

Let number of balcony seats = z

As per given statement, total seats are 800

Sales price of each orchestra seat = $40

Sales price of each main seat = $30

Sales price of each balcony seat = $20

If all the seats are sold, total revenue is $23200.

If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $ 20 comma 000.

Here, we have 3 variables and 3 equations. Let us solve them.

Subtracting Equation (3) from equation (2):

Putting value of x in equations (1) and (2):

Equation (1)

Equation (2)

Equation (5) - 2 Equation(4):

Putting value of y in equation (4):

Hence, answer is:

orchestra seats: main seats: balcony seats: 160: 400: 240

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step-by-step explanation:

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