document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202233>Question 202233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A broadway theatre has 500 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $40, main seats for $25, and balcony seats for $20. If all the seats are sold, the gross revenue to the theatre is $13,150. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $11,150. How many are there of each kind of seat? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152641 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=152641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A Broadway theater has 500 seats, divided into orchestra, main, and balcony seating. <BR>\n" );
document.write( "Orchestra seats sell for $40, main seats for $25, and balcony seats for $20.<BR>\n" );
document.write( " If all the seats are sold, the gross revenue to the theatre is $13,150. <BR>\n" );
document.write( "If all the main and balcony seats are sold, but only half the orchestra seats are sold,<BR>\n" );
document.write( " the gross revenue is $11,150. <BR>\n" );
document.write( "How many are there of each kind of seat?<BR>\n" );
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document.write( "Let x = Orchestra seats<BR>\n" );
document.write( "Let y = Main seats<BR>\n" );
document.write( "Let z = Balcony seats<BR>\n" );
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document.write( "Write an equation for each statement:<BR>\n" );
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document.write( "\"A Broadway theater has 500 seats, divided into orchestra, main, and balcony seating.\"<BR>\n" );
document.write( "x + y + z = 500<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"Orchestra seats sell for $40, main seats for $25, and balcony seats for $20.<BR>\n" );
document.write( " If all the seats are sold, the gross revenue to the theatre is $13,150.\"<BR>\n" );
document.write( "40x + 25y + 20z = 13150<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"but if only half the orchestra seats are sold, the gross revenue is $11,150.\"<BR>\n" );
document.write( "40(.5x) + 25y + 20z = 11150<BR>\n" );
document.write( "20x + 25y + 20z = 11150<BR>\n" );
document.write( ":<BR>\n" );
document.write( "use elimination on these two equations<BR>\n" );
document.write( "40x + 25y + 20z = 13150<BR>\n" );
document.write( "20x + 25y + 20z = 11150<BR>\n" );
document.write( "-------------------------subtraction eliminates y and z<BR>\n" );
document.write( "20x = 2000<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000%2F20 ALIGN=MIDDLE  ALT=\"2000%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 100 orchestra seats<BR>\n" );
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document.write( "Using this value for x, write two equations with two unknowns.<BR>\n" );
document.write( "100 + y + z = 500<BR>\n" );
document.write( "y + z = 500 - 100<BR>\n" );
document.write( "y + z = 400<BR>\n" );
document.write( "and<BR>\n" );
document.write( "40(100) + 25y + 20z = 13150<BR>\n" );
document.write( "4000 + 25y + 20z = 13150<BR>\n" );
document.write( "25y + 20z = 13150 - 4000<BR>\n" );
document.write( "25y + 20z = 9150<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply the 1st equation by 20 and subtract from the above equation<BR>\n" );
document.write( "25y + 20z = 9150<BR>\n" );
document.write( "20y + 20z = 8000<BR>\n" );
document.write( "-------------------subtraction eliminates z<BR>\n" );
document.write( "5y = 1150<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1150%2F5 ALIGN=MIDDLE  ALT=\"1150%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 230 Main seats<BR>\n" );
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document.write( "Find the number of Balcony seats using the total seat equation:<BR>\n" );
document.write( "100 + 230 + z = 500<BR>\n" );
document.write( "z = 500 - 330<BR>\n" );
document.write( "z = 170 Balcony seats<BR>\n" );
document.write( ";<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Check our solutions by finding the total revenue<BR>\n" );
document.write( "40*100 = 4000<BR>\n" );
document.write( "25*230 = 5750<BR>\n" );
document.write( "20*170 = 3400<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "total = 13150; confirms our solutions<BR>\n" );
document.write( ";<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Did this make sense to you? </SPAN>\n" );
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