document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187207>Question 1187207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two numbers is 7. The larger reciprocal exceeds the smaller one by 7/3. Find the numbers<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818149 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x and y are the two numbers<BR>\n" );
document.write( "1/x and 1/y are their respective reciprocals<BR>\n" );
document.write( "Let x > y<BR>\n" );
document.write( "The reciprocal operation will flip the inequality sign<BR>\n" );
document.write( "1/x < 1/y\r<BR>\n" );
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document.write( "Example: 5 > 2 leads to 1/5 < 1/2 aka 0.2 < 0.5\r<BR>\n" );
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document.write( "The larger reciprocal (1/y) exceeds the smaller one (1/x) by 7/3<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "1/y = 1/x + 7/3<BR>\n" );
document.write( "1/y = 3/(3x) + (7x)/(3x)<BR>\n" );
document.write( "1/y = (3+7x)/(3x)\r<BR>\n" );
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document.write( "The sum of the reciprocals is 7<BR>\n" );
document.write( "1/x + 1/y = 7<BR>\n" );
document.write( "1/x + (3+7x)/(3x) = 7<BR>\n" );
document.write( "3/(3x) + (3+7x)/(3x) = 7<BR>\n" );
document.write( "(3+3+7x)/(3x) = 7<BR>\n" );
document.write( "(6+7x)/(3x) = 7<BR>\n" );
document.write( "6+7x = 3x*7<BR>\n" );
document.write( "6+7x = 21x<BR>\n" );
document.write( "6 = 21x-7x<BR>\n" );
document.write( "6 = 14x<BR>\n" );
document.write( "14x = 6<BR>\n" );
document.write( "x = 6/14<BR>\n" );
document.write( "x = (2*3)/(2*7)<BR>\n" );
document.write( "x = <font color=red>3/7 is one of the numbers</font><BR>\n" );
document.write( "1/x = 7/3\r<BR>\n" );
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document.write( "We'll use that value to find the following<BR>\n" );
document.write( "1/y = (1/x) + 7/3<BR>\n" );
document.write( "1/y = 7/3 + 7/3<BR>\n" );
document.write( "1/y = 14/3<BR>\n" );
document.write( "y = <font color=red>3/14 is the other number</font>\r<BR>\n" );
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document.write( "Note that,<BR>\n" );
document.write( "1/x + 1/y = 7/3 + 14/3 = (7+14)/3 = 21/3 = 7<BR>\n" );
document.write( "which helps confirm we have the correct x & y values.\r<BR>\n" );
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document.write( "Answers: <font color=red>3/7 and 3/14</font><BR>\n" );
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