Question

A local theater seats 360 people. They can earn $15,150 when every seat is sold out. If floor seats cost $45 and balcony tickets cost $35, find the number of floor seats and the number of balcony seats in the theater.

Answer 1

The theater has 255 floor seats and 105 balcony seats.

Step-by-step explanation:

To find the number of floor seats and balcony seats in the theater, we can set up a system of equations based on the price of the tickets and the total revenue when the theater is sold out.

Let's assume the number of floor seats is x and the number of balcony seats is y.

The revenue from floor seats would be 45x, and the revenue from balcony seats would be 35y. So we have the equation 45x + 35y = 15150.

The total number of seats in the theater is 360, so we also have the equation x + y = 360.

We can solve this system of equations to find the values of x and y.

Let's solve the second equation for x: x = 360 - y.

Substituting this value of x into the first equation: 45(360 - y) + 35y = 15150.

Simplifying the equation, we get: 16200 - 45y + 35y = 15150.

Combining like terms, we have: -10y = -1050.

Dividing both sides of the equation by -10, we get: y = 105.

Substituting this value of y into the equation x = 360 - y, we get: x = 360 - 105 = 255.

Therefore, there are 255 floor seats and 105 balcony seats in the theater.