document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130340>Question 1130340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ratio of the number of boys to the number of girls in a theater is 7:9. There are 12 more girls than boys in the theater. How many children are in the theater. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747000 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=747000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let b number of boys.<BR>\n" );
document.write( "let g = number of girls.\r<BR>\n" );
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document.write( "ratio of boys to girls is 7:9.\r<BR>\n" );
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document.write( "equation for that is b/g = 7/9\r<BR>\n" );
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document.write( "in the theater, there are 12 more girls than boys.\r<BR>\n" );
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document.write( "equation for that is g = b + 12\r<BR>\n" );
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document.write( "these two equations need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "b/g = 7/9<BR>\n" );
document.write( "g = b + 12\r<BR>\n" );
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document.write( "in the first equation, replace g with b + 12 from the second equation to get:\r<BR>\n" );
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document.write( "b/(b + 12) = 7/9\r<BR>\n" );
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document.write( "cross multiply to get 9b = 7 * (b + 12)\r<BR>\n" );
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document.write( "simplify to get 9b = 7b + 84\r<BR>\n" );
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document.write( "subtract 7b from both sides of the equation to get 2b = 84\r<BR>\n" );
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document.write( "solve for b to get b = 42\r<BR>\n" );
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document.write( "since g = b + 12, then g = 54.\r<BR>\n" );
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document.write( "the number of boys in the theater is 42 and the number of girls in the theater is 54.\r<BR>\n" );
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document.write( "the number of children in the theater is 42 + 54 = 96\r<BR>\n" );
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document.write( "the ratio of boys to girls in the theater is 42 / 54.\r<BR>\n" );
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document.write( "divide numerator and denominator by 6 to get the ratio of boys to girls in the theater is 7 / 9.\r<BR>\n" );
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document.write( "54 - 42 = 12 which means there are 12 more girls in the theater than boys.\r<BR>\n" );
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document.write( "your solution is that the number of children in the theater is 96.\r<BR>\n" );
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document.write( "since the ratio of boys to girls is 7 / 9, this means that, out of every 15 students, 7 are boys and 9 are girls.\r<BR>\n" );
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document.write( "the ratio of boys to total children in the theater is therefore 7 / 15.\r<BR>\n" );
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document.write( "the ratio of girls to total children in the theater is therefore 9 / 15.\r<BR>\n" );
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document.write( "7/15 * 96 = 42.\r<BR>\n" );
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document.write( "9/15 * 96 = 54.\r<BR>\n" );
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document.write( "it all checks out, so the solution is assumed to be good.\r<BR>\n" );
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document.write( "solution is 96 children in the theater.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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