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I have a poll with two options, it does not display the number of votes cast. prior to casting a vote, the ratio was 91.5% to 8.5%. After a single vote cast, the percentages moved to 91.7% and 8.3%.

How many people have answered the poll?

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  1. Suppose that originally there are $n$ people choosing the first response, then the new vote must be the first response since this proportion has increased.

  2. Suppose there are $m$ people choosing the second response. Then the proportion of people choosing response one before the vote is $n/(m+n)$ and you know what the value is of this proportion. The same argument can be used for the situation after the vote.

  3. Using the equations derived in 2., they can be solved for $m$ and $n$.

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