Theater Revenue Math Problem?

Can anyone please help me figure out how to solve this problem. I need step by step instructions! Thanks in advance!

A theater has 600 seats, divided into orchestra, main floor, and balcony seating. Orchestra seats sell for $80, main floor seats for $60 and balcony seats for $25. If all the seats are sold, the total revenue to the theater is $33,500. One evening, all the orchestra seats were sold, 3/5th of the main seats were sold, and 4/5th of the balcony seats were sold. The total revenue collected was $24,640. How many are there of each kind of seat?

1 Answer

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  • 9 years ago
    Best Answer

    o + m + b = 600

    80o + 60m + 25b = 33500

    80o + 60*(3/5)*m + 25*(4/5)*b = 24640, i.e. 80o + 36m + 20b = 24640

    Subtract those last two equations:

    24m + 5b = 8860, call that equation 4

    Multiply the first equation by 80:

    80o + 80m + 80b = 48000

    Subtract the second equation from that:

    20m + 55b = 14500, call that equation 5

    Multiply equation 4 by 11:

    264m + 55b = 97460

    Subtract equation 5 from that:

    244m = 82960

    m = 82960/244

    m = 340

    Substitute that into equation 4:

    24m + 5b = 8860

    24(340) + 5b = 8860

    8160 + 5b = 8860

    5b = 8860 - 8160

    5b = 700

    b = 700/5

    b = 140

    Substitute m and b into equation 1:

    o + 340 + 140 = 600

    o = 600 - 340 - 140

    o = 120

    See also http://jeff.aaron.ca/cgi-bin/equations

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