document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82605>Question 82605</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In local election 2 candidates stood for office.<BR>\n" );
document.write( "After results the loser concluded by saying \"The winning margin of my opponent<BR>\n" );
document.write( "was a mere 6 2/3% (six and two thirds percent) of the Total votes\"<BR>\n" );
document.write( "The loser also said that if he could have persuaded 12 people to vote for him instead of his opponent then he would have won office by a mere 1 vote.<BR>\n" );
document.write( "How many voted for each candidate???<BR>\n" );
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document.write( "So far i get the following<BR>\n" );
document.write( "TOTALvotes=X votes + Y votes<BR>\n" );
document.write( "Winning margin =(20/3)% x TOTALvotes = 0.0666666 x TOTALvotes<BR>\n" );
document.write( "(LOSERvotes + 12)-(WINNERvotes - 12)=1<BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "I dont know how to proceed any further. Can you please assist? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59194 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=59194\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> After results the loser concluded by saying \"The winning margin of my opponent<BR>\n" );
document.write( "was a mere 6 2/3% (six and two thirds percent) of the Total votes\"<BR>\n" );
document.write( "The loser also said that if he could have persuaded 12 people to vote for him instead of his opponent then he would have won office by a mere 1 vote.<BR>\n" );
document.write( "How many voted for each candidate???<BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "Let \"t\" be the total number of votes.<BR>\n" );
document.write( "Winner received (50+(1/2)0.06666=0.533333% of the vote = 0.53333333t votes<BR>\n" );
document.write( "loser received (50%-(1/2)0.0666666)=0.466666 of the vote = 0.46666t votes<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "EQUATION: <BR>\n" );
document.write( "(loser +12) - (winner - 12) =1<BR>\n" );
document.write( "loser-winner+24=1<BR>\n" );
document.write( "(0.46666-0.5333333)t+24=1<BR>\n" );
document.write( "-0.6666666t = -25<BR>\n" );
document.write( "t=375\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.13333t = 25<BR>\n" );
document.write( "t = 187+<BR>\n" );
document.write( "Rounding up: t=188<BR>\n" );
document.write( "==========<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );