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

Answers ( )

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    2021-10-15T16:10:55+00:00

    Answer:

    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

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