To calculate: The number of orchestra, main and balcony seats in a Broadway theater with a total capacity of 500 seats divided in to orchestra, main and balcony. The selling price for orchestra, main and balcony seats are $50, $35, and $25 respectively. The gross revenue is $17100 with all the seats have sold. The gross revenue is $14600 with all the main and balcony seats are sold, but only half of orchestra seats are sold.
Answer to Problem 60AYU
There are 100 orchestra, 210 main and 190 balcony seats in a Broadway theater with a total capacity of 500 seats.
Explanation of Solution
Given information:
It is given that A Broadway Theater has 500 seats, divided in to orchestra, main and balcony. The selling price for orchestra, main and balcony seats are $50, $35, and $25 respectively. The gross revenue is $17100 with all the seats have sold. The gross revenue is $14600 with all the main and balcony seats are sold, but only half of orchestra seats are sold.
Calculation:
Consider the given information that total capacity of 500 seats.
Now, let
Since, the total numbers of seats are 500. So,
Since, the total revenue is $17100. So,
Since, the gross revenue is $14600 with all the main and balcony seats are sold, but only half of orchestra seats are sold So,
Now, system of equation is,
Now, solve first and second equation as,
Now, subtract third equation from second equation in the initial system of equation as,
Substitute x in the equation
Next is,
Therefore, there are 100 orchestra, 210 main and 190 balcony seats in a Broadway theater with a total capacity of 500 seats.
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