document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030371>Question 1030371</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $54, balcony tickets are $46, and mezzanine tickets are $41. One particular night, sales totaled $106,263. There were 482 more main floor tickets sold than balcony and mezzanine tickets combined.  The number of balcony tickets sold is 198 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645222 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=645222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $54, balcony tickets are $46, and mezzanine tickets are $41. One particular night, sales totaled $106,263. There were 482 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 198 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold? <BR>\n" );
document.write( "------\r<BR>\n" );
document.write( "\n" );
document.write( "Equations:<BR>\n" );
document.write( "54m + 46b + 41z = 106,263<BR>\n" );
document.write( "m = b + z + 482<BR>\n" );
document.write( "b = 3z + 198<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Substitute for \"b\" to get m = 4z + 680<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Substitute for m and b and solve for \"z\"::<BR>\n" );
document.write( "54(4z+680) + 46(3z+198) + 41z = 106263<BR>\n" );
document.write( "-------------------------------------------<BR>\n" );
document.write( "216z + 36720 + 138z + 9108 + 41z = 106263<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "395z + 45828 = 106263<BR>\n" );
document.write( "395z = 60435<BR>\n" );
document.write( "z = 153 (# of mezzanine sold)<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Solve for \"b\" and for \"m\" using z = 153<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );