Algebra.Com's Answer #801213 by ikleyn(52756)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "A Broadway theater has 600 seats, divided into orchestra, main, and balcony seating.
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document.write( "Orchestra seats sell for $60 main seats for $50 and balcony seats for $30.
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document.write( "If all the seats are sold, the gross revenue to the theater is $27,000
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document.write( "If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $23,400
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document.write( "How many are there of each kind of seat?
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document.write( "From the condition, half the orchestra seats cost 27000 - 23400 = 3600 dollars.\r\n" );
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document.write( "Thus the half the number of orchestra seats is  = 60, \r\n" );
document.write( "and full number of orchestra seats is 2*60 = 120.\r\n" );
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document.write( "Part of the problem is just solved.\r\n" );
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document.write( "For the other part, we have \r\n" );
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document.write( " - the cost of main and balcony seats total of 23400-3600 = 19800 dollars, and \r\n" );
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document.write( " - the total of these two types of seats is 600-120 = 480.\r\n" );
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document.write( "Let x be the number of main seats; then the number of the balcony seats is (480-x).\r\n" );
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document.write( "Then we write the money equation for these two types of seats\r\n" );
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document.write( " 50*x + 30*(480-x) = 19800 dollars.\r\n" );
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document.write( "From this equation x =  = 270.\r\n" );
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document.write( "ANSWER. 120 orchestra seats; 270 main seats and the rest 600-120-270 = 210 seats.\r\n" );
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document.write( "Solved.\r
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