document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130446>Question 1130446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve and verify your answer. \r<BR>\n" );
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document.write( "The sum of the reciprocals of two consecutive even integers is 9 / 40. Find the integers (smaller and larger integers). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747163 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=747163\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A formal algebraic solution as shown by the other tutor is of course valid.  But if an algebraic solution is not required, solve the problem by logical reasoning and a bit of mental arithmetic, knowing that the numbers are even integers.<br><BR>\n" );
document.write( "Half the sum of the reciprocals is 9/80, which is about 1/9.  So try 8 and 10 as the two consecutive even integers.  They work; so they are the answers.<br><BR>\n" );
document.write( "And here is another way to solve the problem using logical reasoning.  The reciprocals of the two even integers, added together, yield a fraction with denominator 40.  So a more advanced student might also solve the problem by finding two consecutive even integers whose least common multiple is 40; the answer is again 8 and 10. </SPAN>\n" );
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