document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=641184>Question 641184</A>: <I><SPAN STYLE=\"word-break: break-all;\"> one number is 3 times another. the sum of their reciprocals is 20/3. find the numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #403573 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=403573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve, let's turn the sentences into equations.  The first sentence says that one number is 3 times another.  In other words:\r<BR>\n" );
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document.write( "x = 3y\r<BR>\n" );
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document.write( "The next sentence says that the sum of their reciprocals is 20/3. In other words:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx+%2B+1%2Fy+=+20%2F3 ALIGN=MIDDLE  ALT=\"1%2Fx+%2B+1%2Fy+=+20%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To solve, we need to substitute x in the second equation, with 3y, that way we will get rid of x and solve for y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3y+%2B+1%2Fy+=+20%2F3 ALIGN=MIDDLE  ALT=\"1%2F3y+%2B+1%2Fy+=+20%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, multiply the equation by 3y.  This will get rid of our fractions and leave us with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+3+=+20y ALIGN=MIDDLE  ALT=\"1+%2B+3+=+20y\"   DISABLED_style= \"max-width:90%; height:auto;\" > =\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+20y ALIGN=MIDDLE  ALT=\"4+=+20y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides of the equation by 20, and this will leave us with y, which will be one of our numbers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4%2F20 ALIGN=MIDDLE  ALT=\"y+=+4%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1%2F5 ALIGN=MIDDLE  ALT=\"y+=+1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, 1/5 is one of our numbers.  \r<BR>\n" );
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document.write( "We know that the other number is 3 times y.  So, 3 x 1/5 will give us our other number:\r<BR>\n" );
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document.write( "3 x 1/5 = 3/5\r<BR>\n" );
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document.write( "FINAL ANSWER:  1/5 and 3/5 are the numbers </SPAN>\n" );
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