document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=316802>Question 316802</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two distinct integers, m and n, are chosen from the set {1, 2, 3, 4, … , 2009}. What is the maximum possible value of (2m + n) ÷ (m – 2n)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #226741 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=226741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the largest value of a fraction, choose the maximum value for the numerator divided by the minimum value for the denominator.<BR>\n" );
document.write( "If the denominator was zero, the value of the fraction would be infinite. <BR>\n" );
document.write( "In that case,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m-2n=0 ALIGN=MIDDLE  ALT=\"m-2n=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2n ALIGN=MIDDLE  ALT=\"m=2n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the maximum value m can take on is 2009. <BR>\n" );
document.write( "Let's use the closest value to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2F2 ALIGN=MIDDLE  ALT=\"m%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1004 ALIGN=MIDDLE  ALT=\"n=1004\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m-2n=1 ALIGN=MIDDLE  ALT=\"m-2n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%2Bn=5022 ALIGN=MIDDLE  ALT=\"2m%2Bn=5022\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282m%2Bn%29%2F%28m-2n%29=5022 ALIGN=MIDDLE  ALT=\"%282m%2Bn%29%2F%28m-2n%29=5022\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2009 ALIGN=MIDDLE  ALT=\"m=2009\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1004 ALIGN=MIDDLE  ALT=\"n=1004\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );