document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=465204>Question 465204</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average (arithmetic mean) of the test scores of a class of \"p\" students is 70, and the average of the test scores of a class of \"n\" students is 92.  When the scores of both classes are combined, the average score is 86. What is the value of \"p/n\"?\r<BR>\n" );
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document.write( "The answer is 3/8 or .375, but I do not understand how they got this answer.  Can you help? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318813 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=318813\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know that the sum of the scores from the p students is 70p, and the sum of the scores from the n students is 92n. Combining them,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{70p + 92n}{p+n} = 86\">\r<BR>\n" );
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document.write( "We can split up the fraction two ways:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{70p + 92n}{p+n} = \frac{70(p+n)}{p+n} + \frac{22n}{p+n} = 86 \Rightarrow \frac{22n}{p+n} = 16\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{70p + 92n}{p+n} = \frac{92(p+n)}{p+n} - \frac{22p}{p+n} = 86 \Rightarrow \frac{22p}{p+n} = 6\">\r<BR>\n" );
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document.write( "Hence, we are given\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{22p}{p+n} = 6\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{22n}{p+n} = 16\">\r<BR>\n" );
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document.write( "If we divide the first equation by the second, the 22's and the p+n's will cancel, and we will get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{p}{n} = \frac{6}{16} = \frac{3}{8}\">. </SPAN>\n" );
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