document.write( "Question 1118783:
\n" ); document.write( "
\n" ); document.write( "Problema Solution \r
\n" ); document.write( "\n" ); document.write( "A Broadway theater has 700 seats, divided into orchestra,main and balcony seating. Orchestra seats sell for $40, main seats sell for $25, and balcony seats for $20. If all the seats are sold, the gross revenue to the theater is $18,400. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $15,600. How many are there of each kind of seat? \n" ); document.write( "

Algebra.Com's Answer #734209 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "After reading the condition, you should notice momentarily that half of the orchestra seats costs 18400 - 15600 = 2800 dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, the half of the orchestra seats is  = 70 seats, and the entire number of the orchestra seats is 2*70 = 140.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus you just can reduce the original problem to the simpler one:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     There are 700-140 = 560 seats; of them, main seats sell for $25 and balcony seats sell for $20.\r\n" );
document.write( "\r\n" );
document.write( "     The revenue obtained for main seats and balcony seats is  18400 - 140*40 = 12800 dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You can solve this problem as an two-unknown problem or even as an one-unknown problem, on your choice.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I prefer one-unknown, as it is shown below.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let x be the number of main seats.\r\n" );
document.write( "\r\n" );
document.write( "Then the number of balcony seats is  (560-x).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The money equation for this reduced problem is\r\n" );
document.write( "\r\n" );
document.write( "25x + 20*(560-x) = 12800    dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and solve for x:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "25x + 20*560 - 20x = 12800\r\n" );
document.write( "\r\n" );
document.write( "25x - 20x = 12800 - 20*560 = 1600\r\n" );
document.write( "\r\n" );
document.write( "5x = 1600  ====>  x =  = 320.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  140 orchestra seats, 320 main seats and  (560-320) = 240 balcony seats.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );