document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=229118>Question 229118</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The smaller of two numbers is two-thirds of the larger, and the sum of their reciprocals is 1/6. What are 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 #169939 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=169939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> S = smaller number<BR>\n" );
document.write( "L = larger number\r<BR>\n" );
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document.write( "S = 2L/3 (equation 1)\r<BR>\n" );
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document.write( "1/S + 1/L = 1/6 (equation 2)\r<BR>\n" );
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document.write( "Multiply both sides of equation 2 by S*L.\r<BR>\n" );
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document.write( "1/S + 1/L = 1/6 becomes:\r<BR>\n" );
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document.write( "L + S = (S*L)/6\r<BR>\n" );
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document.write( "Multiply both sides of this equation by 6 to get:\r<BR>\n" );
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document.write( "6L + 6S = S*L\r<BR>\n" );
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document.write( "Replace S with (2L)/3 to get:\r<BR>\n" );
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document.write( "6L + 6*(2L)/3 = L*2L/3\r<BR>\n" );
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document.write( "Remove Parentheses to get:\r<BR>\n" );
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document.write( "6L + 12L/3 = 2L^2/3\r<BR>\n" );
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document.write( "Multiply both sides of equation by 3 to get:\r<BR>\n" );
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document.write( "18L + 12L = 2L^2\r<BR>\n" );
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document.write( "Combine like terms to get:\r<BR>\n" );
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document.write( "30L = 2L^2\r<BR>\n" );
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document.write( "Divide both sides of equation by 2 to get:\r<BR>\n" );
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document.write( "15L = L^2\r<BR>\n" );
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document.write( "Subttract 15L from both sides of equation to get:\r<BR>\n" );
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document.write( "L^2 - 15L = 0\r<BR>\n" );
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document.write( "Factor L to get:\r<BR>\n" );
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document.write( "L*(L-15) = 0\r<BR>\n" );
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document.write( "Solve for L to get:\r<BR>\n" );
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document.write( "L = 0<BR>\n" );
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document.write( "L = 15\r<BR>\n" );
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document.write( "Substitute these in original equations to get:\r<BR>\n" );
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document.write( "S = 2L/3 becomes:\r<BR>\n" );
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document.write( "S = 2*0/3 = 0<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "S = 2*15/3 = 10\r<BR>\n" );
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document.write( "When S = 0 and L = 0, then 1/S + 1/L = 1/6 becomes:\r<BR>\n" );
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document.write( "1/0 + 1/0 = 1/6 which is false so L = 0 is not a valid answer and can be rejected.\r<BR>\n" );
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document.write( "When S = 10 and L = 15, then 1/10 + 1/15 = 1/6.\r<BR>\n" );
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document.write( "Multiply both sides of of this equation by 30 to get:\r<BR>\n" );
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document.write( "3 + 2 = 5 which is true so L = 15 is good.\r<BR>\n" );
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document.write( "Your answer is L = 15 and S = 10.\r<BR>\n" );
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document.write( "The larger number is 15 and the smaller number is 10.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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