document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=479892>Question 479892</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of a rational number (fraction) and its reciprocal is equal to some positive integer plus 69/110. What is the integer? choose the answer and explain the reason to choose your response <BR>\n" );
document.write( "5 <BR>\n" );
document.write( "2<BR>\n" );
document.write( " 4 <BR>\n" );
document.write( "3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #328928 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=328928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> No one seems to want this problem and I am not too happy with this effort but here it is:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = the rational number<BR>\n" );
document.write( "Let y = \"some positive integer\"<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The sum of a rational number (fraction) and its reciprocal is equal to some positive integer plus 69/110.<BR>\n" );
document.write( "x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = y + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=69%2F110 ALIGN=MIDDLE  ALT=\"69%2F110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Only y = 4, seems to work out for me here<BR>\n" );
document.write( "x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=69%2F110 ALIGN=MIDDLE  ALT=\"69%2F110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=440%2F110 ALIGN=MIDDLE  ALT=\"440%2F110\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=69%2F110 ALIGN=MIDDLE  ALT=\"69%2F110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=509%2F110 ALIGN=MIDDLE  ALT=\"509%2F110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find x<BR>\n" );
document.write( "x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=509%2F110 ALIGN=MIDDLE  ALT=\"509%2F110\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0<BR>\n" );
document.write( "Multiply by 110x<BR>\n" );
document.write( "110x^2 - 509x + 110 = 0<BR>\n" );
document.write( "Using the quadratic formula: a=110, b=-509, c=110<BR>\n" );
document.write( "One solution that works x = 4.4 which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44%2F10 ALIGN=MIDDLE  ALT=\"44%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > so we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44%2F10 ALIGN=MIDDLE  ALT=\"44%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F44 ALIGN=MIDDLE  ALT=\"10%2F44\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=69%2F110 ALIGN=MIDDLE  ALT=\"69%2F110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Checking it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=968%2F220 ALIGN=MIDDLE  ALT=\"968%2F220\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2F220%29+=+%7B%7B%7B880%2F220 ALIGN=MIDDLE  ALT=\"50%2F220%29+=+%7B%7B%7B880%2F220\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=138%2F220 ALIGN=MIDDLE  ALT=\"138%2F220\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1018%2F220 ALIGN=MIDDLE  ALT=\"1018%2F220\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1018%2F220 ALIGN=MIDDLE  ALT=\"1018%2F220\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );