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Question 13

In an election $$320$$ votes were cast for five candidates. The winner's margins over the other four candidates were $$9,13,18$$ and $$25$$. The lowest number of votes received by a candidate was

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Let the winner receive $$x$$ votes. The other four candidates then receive $$x-9,x-13,x-18,x-25$$ votes. Thus $$5x-65=320$$, giving $$x=77$$. The lowest count is $$77-25=52$$.

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