document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891431>Question 891431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an election contested between A and B,  A obtained votes equal to twice the no. Of persons on the electoral roll who didn't cast their votes and this later no. Was equal to twice his majority over B. If there were 18000 persons or the electoral roll how many voted for B </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539735 by </B><A HREF=/tutors/aboutme.mpl?userid=JulietG><B>JulietG(1812)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JulietG><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=JulietG><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are three categories:<BR>\n" );
document.write( "Those who voted for A<BR>\n" );
document.write( "Those who voted for B<BR>\n" );
document.write( "Those who did not vote (we'll call this \"C\")<BR>\n" );
document.write( "A = 2C [A obtained votes equal to twice the no. Of persons on the electoral roll who didn't cast their votes]<BR>\n" );
document.write( "C = 2(A-B) [this later no. Was equal to twice his majority over B] C = 2A - 2B<BR>\n" );
document.write( "A + B + C = 18,000<BR>\n" );
document.write( "Substitute the value of C from the second equation into the first.<BR>\n" );
document.write( "A = 2(2A-2B)<BR>\n" );
document.write( "Distribute<BR>\n" );
document.write( "A = 4A-4B<BR>\n" );
document.write( "Add 4 B to each side<BR>\n" );
document.write( "4B = 4A - A<BR>\n" );
document.write( "4B = 3A<BR>\n" );
document.write( "Divide each side by 4<BR>\n" );
document.write( "B = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >A  [Let's change it to .75A for ease of use]<BR>\n" );
document.write( "B = .75A<BR>\n" );
document.write( "C = 2(A-B) or C = 2A - 1.5A (twice B)<BR>\n" );
document.write( "C = .5A<BR>\n" );
document.write( "Back to A + B + C = 18,000<BR>\n" );
document.write( "A + .75A + .5A = 18,000<BR>\n" );
document.write( "2.25A = 18,000<BR>\n" );
document.write( "Divide each side by 2.25<BR>\n" );
document.write( "A = 8000<BR>\n" );
document.write( "If A is 8000, then B is .75*8000, or 6,000.  C is half of A, so 4,000.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A wins the election.  Unless, of course, it's being held in <a  rel=nofollow HREF=http://www.heritage.org/research/reports/2008/04/where-theres-smoke-theres-fire-100000-stolen-votes-in-chicago>Chicago.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );