## A Broadway theater has 700 ​seats, divided into​ orchestra, main, and balcony seating. Orchestra seats sell for \$ 50 comma main seats for \$

Question

A Broadway theater has 700 ​seats, divided into​ orchestra, main, and balcony seating. Orchestra seats sell for \$ 50 comma main seats for \$ 40 comma and balcony seats for \$ 25.  If all the seats are​ sold, the gross revenue to the theater is \$ 26 comma 250.  If all the main and balcony seats are​ sold, but only half the orchestra seats are​ sold, the gross revenue is \$ 22 comma 750. How many are there of each kind of​ seat?There are orchestra​ seats?
main​ seats?
balcony seats?

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2 months 2021-10-15T16:09:09+00:00 1 Answer 0 views 0

orchestra​ seats = 140 seats

main​ seats = 350 seats

balcony seats = 210 seats

Step-by-step explanation:

Let x = number of orchestra seats

Let y = number of main seats

Let z = number of balcony seats

Theater has 700 seats. Thus;

Total seat equation is;

x + y + z = 700 – – – – (1)

We are told Orchestra seats sell for \$ 50, main seats for \$ 40, and balcony seats for \$ 25 and a gross revenue of \$26,250

Thus ;

all seats revenue equation is;

50x + 40y + 25z = 26250 – – – (eq2)

Now, we are told that, when all the main and balcony seats are​ sold, but only half the orchestra seats are​ sold, the gross revenue is \$ 22,750

Thus, we have;

½(50x) + 40y + 25z = 22,750

Which gives ;

25x + 40y + 25z = 22,750 —(eq3)

Solving the 3 equations simultaneously, we have;

x = 140

y = 350

z = 210