SOLUTION: In local election 2 candidates stood for office. After results the loser concluded by saying "The winning margin of my opponent was a mere 6 2/3% (six and two thirds percent) of

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Question 82605: In local election 2 candidates stood for office.
After results the loser concluded by saying "The winning margin of my opponent
was a mere 6 2/3% (six and two thirds percent) of the Total votes"
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.
How many voted for each candidate???
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So far i get the following
TOTALvotes=X votes + Y votes
Winning margin =(20/3)% x TOTALvotes = 0.0666666 x TOTALvotes
(LOSERvotes + 12)-(WINNERvotes - 12)=1
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I dont know how to proceed any further. Can you please assist?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
After results the loser concluded by saying "The winning margin of my opponent
was a mere 6 2/3% (six and two thirds percent) of the Total votes"
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.
How many voted for each candidate???
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Let "t" be the total number of votes.
Winner received (50+(1/2)0.06666=0.533333% of the vote = 0.53333333t votes
loser received (50%-(1/2)0.0666666)=0.466666 of the vote = 0.46666t votes
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EQUATION:
(loser +12) - (winner - 12) =1
loser-winner+24=1
(0.46666-0.5333333)t+24=1
-0.6666666t = -25
t=375

0.13333t = 25
t = 187+
Rounding up: t=188
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Cheers,
Stan H.