document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78643>Question 78643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Social Science.  Show the equation used for the solution.  In a town election, the winning candidate had 220 more votes than the loser.  If 810 votes were cast in all, how many votes did each candidate receive?  Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56397 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=56397\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let w=winner, L=loser\r<BR>\n" );
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document.write( "If the winner (w) had 220 more votes than the loser (L), then the winner's votes is equal to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=L%2B220 ALIGN=MIDDLE  ALT=\"w=L%2B220\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now if there were 810 votes total, then the winners votes and the losers votes would add to the total like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%2BL=810 ALIGN=MIDDLE  ALT=\"w%2BL=810\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we can substitute L+220 in for w like this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28L%2B220%29%2BL=810 ALIGN=MIDDLE  ALT=\"highlight%28L%2B220%29%2BL=810\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%2B220=810 ALIGN=MIDDLE  ALT=\"2L%2B220=810\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L=590 ALIGN=MIDDLE  ALT=\"2L=590\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 220 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F2%29L=590%2F2 ALIGN=MIDDLE  ALT=\"%282%2F2%29L=590%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=295 ALIGN=MIDDLE  ALT=\"L=295\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "So the loser had 295 votes. Since the winner had 220 more votes than the loser, we can add 220 to 295 to find out how many votes the winner had\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=295%2B220 ALIGN=MIDDLE  ALT=\"w=295%2B220\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=515 ALIGN=MIDDLE  ALT=\"w=515\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the winner had 515 votes while the loser had 295 votes\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "One way to check this is to add the winner's and the loser's votes together (we should get 810):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%2BL=810 ALIGN=MIDDLE  ALT=\"w%2BL=810\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in w=515,L=295<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=515%2B295=810 ALIGN=MIDDLE  ALT=\"515%2B295=810\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=810=810 ALIGN=MIDDLE  ALT=\"810=810\"   DISABLED_style= \"max-width:90%; height:auto;\" > works. So this verifies our answer. </SPAN>\n" );
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