document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=287564>Question 287564</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Broadway theater has 700 seats, divided into orchestra, main, and balcony seating. Orchestra seats sells for $40, Main for $30, and balcony for $20. If all seats are sold the gross revenue is $20,200. If all main and balcony seats are sold, but only half of the orchestra is sold, the gross revenue is $17,400. How many seats are there of each kind?<BR>\n" );
document.write( "Orchestra-<BR>\n" );
document.write( "Main-<BR>\n" );
document.write( "Balcony- </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #208898 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=208898\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A Broadway theater has 700 seats, divided into orchestra, main, and balcony seating. <BR>\n" );
document.write( "Orchestra seats sells for $40, Main for $30, and balcony for $20.<BR>\n" );
document.write( " If all seats are sold the gross revenue is $20,200.<BR>\n" );
document.write( " If all main and balcony seats are sold, but only half of the orchestra is sold,<BR>\n" );
document.write( " the gross revenue is $17,400.<BR>\n" );
document.write( " How many seats are there of each kind?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = no. of orchestra seats<BR>\n" );
document.write( "Let y = no. of main<BR>\n" );
document.write( "Let z = no. of balcony<BR>\n" );
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document.write( "Total seat equation<BR>\n" );
document.write( "x + y + z = 700<BR>\n" );
document.write( ":<BR>\n" );
document.write( "all seats revenue  equation<BR>\n" );
document.write( "40x + 30y + 20z = 20200<BR>\n" );
document.write( ":<BR>\n" );
document.write( "half orch, all main, all balcony revenue equation<BR>\n" );
document.write( "40(.5x) + 30y + 20z = 17400<BR>\n" );
document.write( "20x + 30y + 20z = 17400<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use elimination on the last two equation to find x:<BR>\n" );
document.write( "40x + 30y + 20z = 20200<BR>\n" );
document.write( "20x + 30y + 20z = 17400<BR>\n" );
document.write( "---------------------------subtraction eliminates y and z<BR>\n" );
document.write( "20x = 2800<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2800%2F20 ALIGN=MIDDLE  ALT=\"2800%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 140 orchestra seats<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using the 1st equation, replace x with 140<BR>\n" );
document.write( "140 + y + z = 700<BR>\n" );
document.write( "y + z = 700 - 140<BR>\n" );
document.write( "y + z = 560<BR>\n" );
document.write( "y = (560-z)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using substitution, findz<BR>\n" );
document.write( "40x + 30y + 20z = 20200<BR>\n" );
document.write( "40(140) + 30(560-z) + 20z = 20200<BR>\n" );
document.write( "5600 + 16800 - 30z + 20z = 20200<BR>\n" );
document.write( "22400 - 30z + 20z = 20200<BR>\n" );
document.write( "-10z = 20200 - 22400<BR>\n" );
document.write( "-10z = -2200<BR>\n" );
document.write( "z = +220 balcony seat<BR>\n" );
document.write( ":<BR>\n" );
document.write( "I'll let you find y, the number of main seats<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Orchestra-140<BR>\n" );
document.write( "Main-<BR>\n" );
document.write( "Balcony-220 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );