document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142693>Question 1142693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a school function, 4/9 of the audience was female and the rest were male. 1/3 of the adults are female. If there were 85 male children, how many persons altogether attend the program. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763399 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=763399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number of males in attendance.<BR>\n" );
document.write( "let y = the number of females in attendance.\r<BR>\n" );
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document.write( "x + y = number of people in attendance.\r<BR>\n" );
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document.write( "4/9 * (x + y) = number of females.<BR>\n" );
document.write( "5/9 * (x + y) = number of males.\r<BR>\n" );
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document.write( "you are given that 1/3 of the adults are females.<BR>\n" );
document.write( "this means that 2/3 of the adults have to be male.\r<BR>\n" );
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document.write( "if 2/3 of the adults have to be male, then the number of adult males is equal to 2/3 * 5/9 * (x + y).\r<BR>\n" );
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document.write( "this means that the number of male children has to be equal to 1/3 * 5/9 * (x + y).\r<BR>\n" );
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document.write( "since the number of male children is equal to 85, you get:\r<BR>\n" );
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document.write( "1/3 * 5/9 * (x + y) = 85\r<BR>\n" );
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document.write( "solve for x + y to get x + y = 85 * 3 * 9/5 = 459.\r<BR>\n" );
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document.write( "this implies that the number of people in attendance was 459.\r<BR>\n" );
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document.write( "that should be your solution.\r<BR>\n" );
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document.write( "working through the numbers with the assumption that the total number of attendees is 459, i get the following.\r<BR>\n" );
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document.write( "4/9 * 459 = 204 females in attendance.<BR>\n" );
document.write( "5/9 * 459 = 255 males in attendance.\r<BR>\n" );
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document.write( "of the males in attendance, 85 are children.<BR>\n" );
document.write( "that makes 170 adult males in attendance.\r<BR>\n" );
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document.write( "if 1/3 of the adults in attendance are female, then 2/3 of the adults in attendance have to be male.<BR>\n" );
document.write( "let z = number of adults, then you get 2/3 * z = 170.<BR>\n" );
document.write( "that makes z = 170 * 3/2 = 255.\r<BR>\n" );
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document.write( "this means that 255 of the attendees are adults.<BR>\n" );
document.write( "170 of them are male.<BR>\n" );
document.write( "85 of them are female.<BR>\n" );
document.write( "1/3 * 255 = 85 (females).<BR>\n" );
document.write( "2/3 * 255 = 170 (males).\r<BR>\n" );
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document.write( "if 85 females are adult, then 204 - 85 = 119 females in attendance are children.\r<BR>\n" );
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document.write( "if you work up a chart, it would look like this.\r<BR>\n" );
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document.write( "                  male          female       total\r\n" );
document.write( "adults            170           85           255\r\n" );
document.write( "children          85            119          204\r\n" );
document.write( "total             255           204          459\r\n" );
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document.write( "ratio of males to total is 255 / 459 = 5/9<BR>\n" );
document.write( "ratio of females to total is 204 / 459 = 4/9<BR>\n" );
document.write( "ratio of female adults to total adults is 85 / 255 = 1/3.<BR>\n" );
document.write( "ratio of male adults to total adults is 170 / 255 = 2/3.\r<BR>\n" );
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document.write( "i'm pretty sure your solution is that the total number of people in attendance is equal to 459.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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