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Problem:

If a candidate Smith trails a candidate Jones by 20K votes, and there's 50K votes still outstanding, what is the percentage needed of the still outstanding 50K votes to overcome Jones?

If:

  • "x" < 1
  • S = number of votes for Smith
  • J = number of votes for Jones

then:

Yes, intuitively I knów the answer (x = 0,7 ), but how do I get there mathematically? Something like:

x * S - (1-x) * J = 20
x * S + (1-x) * J = 50

I don't how to solve 2 equations with 3 unknowns, but I also don't know if that is a good mathematical representation of the problem.

Sara Phina
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1 Answers1

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You don't need to know $S,J$. You are given $J-S=20$ (measuring in thousands). Suppose Smith gets additional $x$ votes, then Jones gets the remaining $50-x$ votes. We need Smith to overcome Jones, so the only relation needed is$$(S+x)>(J+50-x)\\2x>J-S+50=70$$giving $x>35$. So Smith must get more than $35k$ of the remaining votes to beat Jones.

Shubham Johri
  • 17,659