Question

A Broadway theater has 490 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $140, main seats for $135, and balcony seats for $90. If all the seats are sold, the gross revenue to the theater is $59,100. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $50,700. How many of each kind of seat are there? The types of seats are Orchestra, Main Seats, and Balcony Seats

Answer 1

Explanation:

Let's call the number of orchestra seats "O", the number of main seats "M", and the number of balcony seats "B". We can write the following two equations to represent the given information:

O * $140 + M * $135 + B * $90 = $59,100

0.5 * O * $140 + M * $135 + B * $90 = $50,700

Subtracting the second equation from the first, we get:

0.5 * O * $140 = $59,100 - $50,700 = $8,400

Dividing both sides of the equation by 0.5 * $140, we get:

O = $8,400 / ($140 * 0.5) = 30 seats

Substituting this value back into the second equation:

0.5 * 30 * $140 + M * $135 + B * $90 = $50,700

Expanding and simplifying:

$2100 + M * $135 + B * $90 = $50,700

Subtracting $2100 from both sides:

M * $135 + B * $90 = $50,700 - $2100 = $48,600

Dividing both sides of the equation by $135:

M + B = $48,600 / $135 = 360 seats

Finally, since the total number of seats is 490:

M + B + O = 490

Substituting the values of O and M from above:

360 + 30 = 390 + 30 = 490

So there are 360 main seats and 30 balcony seats.