document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=587861>Question 587861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Broadway theater has 400 seats, divided into orchestra, main and balcony seating. Orchestra seats sell for $80, main seats for $60 and balcony seats for $40. If all the seats are sold, the gross revenue to the theater is $23,200. If all the main seats and the balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $20,000. How many are there of each seat? \r<BR>\n" );
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document.write( "I've tried solving this by writing an equation and trying to solve for x but it didn't get me the correct answer, any help would be appreciated. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #374290 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=374290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A Broadway theater has 400 seats, \r<BR>\n" );
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document.write( " orchestra,(x) main (y)and balcony seating(z) \r<BR>\n" );
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document.write( "x+y +z= 400.........................(1)\r<BR>\n" );
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document.write( "Orchestra seats sell for $80, main seats for $60 and balcony seats for $40. If all the seats are sold, the gross revenue to the theater is $23,200. \r<BR>\n" );
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document.write( "80x+60y+40z=23200...................(2)\r<BR>\n" );
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document.write( "If all the main seats and the balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $20,000.\r<BR>\n" );
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document.write( "60y++40z+(x/2) *80 = 20,000<BR>\n" );
document.write( "40x+60y+80z=20,000.................(3)\r<BR>\n" );
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document.write( "80x+60y+40z=23200...................(2)<BR>\n" );
document.write( "rewrite this equation<BR>\n" );
document.write( "40x+(40x+60y+40z)= 23200\r<BR>\n" );
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document.write( "But<BR>\n" );
document.write( "40x+60y+80z=20,000\r<BR>\n" );
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document.write( "so 40x+20000=23200<BR>\n" );
document.write( "40x=23200-20000<BR>\n" );
document.write( "40x = 3200<BR>\n" );
document.write( "/40<BR>\n" );
document.write( "x= 80 seats  that of Orchestra.\r<BR>\n" );
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document.write( "consider equation (1) & (2)<BR>\n" );
document.write( "x+y+z=400<BR>\n" );
document.write( "80+y+z=400<BR>\n" );
document.write( "y+z=400-80<BR>\n" );
document.write( "y+z=320.....................(4)\r<BR>\n" );
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document.write( "80x+60y+40z=23200\r<BR>\n" );
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document.write( "80*80 +60y+40z=23200<BR>\n" );
document.write( "60y+40z= 23200-6400<BR>\n" );
document.write( "60y+40z=16800<BR>\n" );
document.write( "divide by 20<BR>\n" );
document.write( "3y+2z=840...................(5)\r<BR>\n" );
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document.write( "solve equations (4) & (5)<BR>\n" );
document.write( "y+z=320<BR>\n" );
document.write( "3y+2z=840<BR>\n" );
document.write( "multiply (4) by -2 and it to (5)<BR>\n" );
document.write( "-2y-2z=-640<BR>\n" );
document.write( "Add up<BR>\n" );
document.write( "y= 200\r<BR>\n" );
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document.write( "Now x= 80, y =200 so z= 120 \r<BR>\n" );
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document.write( "Check\r<BR>\n" );
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document.write( " 6400+12000+4800= 23200<BR>\n" );
document.write( " </SPAN>\n" );
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