document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=105453>Question 105453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of two numbers is 5 and the sum of their reciprocals is 9/10. 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 #76759 by </B><A HREF=/tutors/aboutme.mpl?userid=checkley75><B>checkley75(3666)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=checkley75><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=76759\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> XY=5 OR X=5/Y<BR>\n" );
document.write( "1/X+1/Y=9/10<BR>\n" );
document.write( "NOW REPLACE X BY 5/Y & SOLVE FOR Y IN THE SECOND EQUATON.<BR>\n" );
document.write( "1/(5/Y)+1/Y=9/10 NOW INVERT THE DENOMINATOR OF THE FIRST FRACTION.<BR>\n" );
document.write( "Y/5+1/Y=9/10 NOW COMBINE THE FRACTIONS.<BR>\n" );
document.write( "(Y*2+5)/5Y=9/10 NOW CROSS MULTIPLY<BR>\n" );
document.write( "10Y^2+50=45Y<BR>\n" );
document.write( "10Y^2-45Y+50=0<BR>\n" );
document.write( "5(2Y^2-9Y+10)=0<BR>\n" );
document.write( "5(2Y-5)(Y-2)=0<BR>\n" );
document.write( "2Y-5=0<BR>\n" );
document.write( "2Y=5<BR>\n" );
document.write( "Y=5/2 OR 2.5 ANSWER<BR>\n" );
document.write( "X*2.5=5<BR>\n" );
document.write( "X=5/2.5<BR>\n" );
document.write( "X=2 ANSWER.<BR>\n" );
document.write( "PROOF<BR>\n" );
document.write( "2*2.5=5<BR>\n" );
document.write( "1/2.5+1/2=9/10<BR>\n" );
document.write( "(5+4)/10=9/10<BR>\n" );
document.write( "9/10=9/10 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );