document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1111018>Question 1111018</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two numbers is 7 and the difference of the reciprocals is 3. 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 #726015 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=726015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You have received two good solutions, very similar to each other, from other tutors.<br><BR>\n" );
document.write( "Here is a suggestion for a different approach you might find easier.<br><BR>\n" );
document.write( "Let the two numbers we are looking be x and y.  We know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%2B1%2Fy+=+7 ALIGN=MIDDLE  ALT=\"1%2Fx%2B1%2Fy+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx-1%2Fy+=+3 ALIGN=MIDDLE  ALT=\"1%2Fx-1%2Fy+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Working with fractions is more difficult than working with whole numbers.  So<br><BR>\n" );
document.write( "let a = 1/x<BR>\n" );
document.write( "let b = 1/y<br><BR>\n" );
document.write( "then the two equations are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb+=+7 ALIGN=MIDDLE  ALT=\"a%2Bb+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b+=+3 ALIGN=MIDDLE  ALT=\"a-b+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That pair of equations is easily solved to find a=5 and b=2.<br><BR>\n" );
document.write( "Then, to finish the original problem,<BR>\n" );
document.write( "x = 1/a = 1/5<BR>\n" );
document.write( "y = 1/b = 1/2<br><BR>\n" );
document.write( "The two numbers are 1/5 and 1/2. </SPAN>\n" );
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