document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=278339>Question 278339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me solve for variation: n varies directly as q, and n=39 when q=3. Find n when q =8. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202542 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=202542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> n varies directly as q.<BR>\n" );
document.write( "n = 39 when q = 3<BR>\n" );
document.write( "find n when q = 8\r<BR>\n" );
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document.write( "n varies directly as q means that n = k*q\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( "39 = k*3\r<BR>\n" );
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document.write( "divide both sides of this equation by 3 to get:\r<BR>\n" );
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document.write( "k = 13\r<BR>\n" );
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document.write( "now that you have the value of k, you can solve for finding n when q = 8\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "n = k*q becomes n = 13*8 which becomes n = 104\r<BR>\n" );
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document.write( "in a direct variation problem, the ratio between n and q remains the same.\r<BR>\n" );
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document.write( "this means that n1 is to q1 as n2 is to q2.\r<BR>\n" );
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document.write( "in formula terms, this would be n1/q1 = n2/q2\r<BR>\n" );
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document.write( "in your problem, this becomes:\r<BR>\n" );
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document.write( "39/3 = 104/8\r<BR>\n" );
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document.write( "cross multiply and you get 39*8 = 3*104 which becomes 312 = 312 confirming that the ratio is the same between the 2 numbers of n/q.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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