document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=916668>Question 916668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello!\r<BR>\n" );
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document.write( "in an election, 2.8 million votes were cast and each vote was for either Candidate 1 or Candidate 2. Candidate 2 received 28,000 more votes than Candidate 1. What percent of the 2.8 million votes were cast for Candidate 1? \r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556204 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=556204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = # of votes for candidate 1 (this number is in millions)<BR>\n" );
document.write( "y = # of votes for candidate 2 (this number is in millions)\r<BR>\n" );
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document.write( "First equation: \r<BR>\n" );
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document.write( "x+y = 2.8\r<BR>\n" );
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document.write( "since a total of \"2.8 million votes were cast and each vote was for either Candidate 1 or Candidate 2\"\r<BR>\n" );
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document.write( "28,000 = 28,000/1,000,000 = 0.028 million\r<BR>\n" );
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document.write( "Second equation:\r<BR>\n" );
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document.write( "y = x + 0.028\r<BR>\n" );
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document.write( "because \"Candidate 2 received 28,000 more votes than Candidate 1\"\r<BR>\n" );
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document.write( "this is the same as saying \"Candidate 2 received 0.028 million more votes than Candidate 1\"\r<BR>\n" );
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document.write( "We'll use substitution to solve for x.\r<BR>\n" );
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document.write( "x+y = 2.8\r<BR>\n" );
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document.write( "x+x + 0.028 = 2.8 ... replace y with x + 0.028\r<BR>\n" );
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document.write( "2x+0.028 = 2.8\r<BR>\n" );
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document.write( "2x = 2.8-0.028\r<BR>\n" );
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document.write( "2x = 2.772\r<BR>\n" );
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document.write( "x = 2.772/2\r<BR>\n" );
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document.write( "x = 1.386\r<BR>\n" );
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document.write( "Remember that x =  # of votes for candidate 1 (this number is in millions)\r<BR>\n" );
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document.write( "Since x = 1.386, this means that Candidate 1 got 1.386 million votes.\r<BR>\n" );
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document.write( "Divide this by 2.8 (the total): 1.386/2.8 = 0.495\r<BR>\n" );
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document.write( "Multiply by 100: 0.495*100 = <font size=5 color=\"red\">49.5%</font>\r<BR>\n" );
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document.write( "So Candidate 1 got <font size=5 color=\"red\">49.5%</font> of the vote. \r<BR>\n" );
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document.write( "Candidate 2 got 100 - 49.5 = 50.5% of the vote. This means Candidate 2 is the winner. This part can be easily determined from the fact that \"Candidate 2 received 28,000 more votes than Candidate 1\". Despite this, it helps to see the percentages as well.\r<BR>\n" );
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document.write( "Let me know if you need more help or if you need me to explain a step in more detail.<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim  </SPAN>\n" );
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