document.write( "Question 441195: A Broadway theater has 600 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $70, main seats for $60, and balcony seats for $35. If all the seats are sold, the gross revenue to the theater is $32,950. If all the main and balcony seats are sold, but only have the orchestra seats are sold, the gross revenue is $28,750. How many are there of each kind of seat? \n" ); document.write( "

Algebra.Com's Answer #304586 by htmentor(1343) $\"\"$ $\"About$

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Let b = the number of balcony seats sold
\n" ); document.write( "Let m = the number of main seats sold
\n" ); document.write( "Then 600 - b - m = the number of orchestra seats sold
\n" ); document.write( "For the gross revenue we can write
\n" ); document.write( "35b + 60m + 70(600 - b - m) = 32950
\n" ); document.write( "If only half the orchestra seats are sold we can write
\n" ); document.write( "35b + 60m + 70(600 - b - m)/2 = 28750
\n" ); document.write( "Simplifying gives:
\n" ); document.write( "35b + 60m + 42000 - 70b - 70m = 32950
\n" ); document.write( "35b + 10m = 9050 [1]
\n" ); document.write( "35b + 60m + 21000 - 35b - 35m = 28750
\n" ); document.write( "25m = 7750 -> m = 310
\n" ); document.write( "Substituting this value for m into [1] gives
\n" ); document.write( "35b + 3100 = 9050 -> b = 170
\n" ); document.write( "So the number of orchestra seats sold is 600 - 170 - 310 = 120
\n" ); document.write( "Ans: Balcony seats = 170; Main seats = 310; Orchestra seats = 120
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