AIME Math Question Help
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[From: ] [author: ] [Date: 12-06-21] [Hit: ]
If we ignore 0 votes for any candidates, which would have 0 % and 0 votes, and /no difference/ no matter how many voters -- what about some getting just 1 vote?1 / 134 = 0.746 %.Compared to 1 vote,......

Okay, so, what number of voters do we need to make 4 votes 3 % of the votes or less?

4/x = 3 %
3x = 400
x = 133 1/3

So, we need full-bodied voters, and must round up.

134 it is. :-)

Uh oh, /BUT/ -- what if some of the candidates got 1 vote?

If we ignore 0 votes for any candidates, which would have 0 % and 0 votes, and /no difference/ no matter how many voters -- what about some getting just 1 vote?

1 / 134 = 0.746 %. Compared to 1 vote, that is /not/ at least 1 more than the percentage.

Again, ignoring 0 votes which will always fail our test, what number of voters would we need for 1 vote received to be "0 percentage"? I guess it depends on how closely you want to round the numbers. We could use 0.49 % as "equaling 0 %". Or, 0.000001 % as "equaling 0 %". Take your pick, we could figure out the number of voters needed to make that approximation for 0 equal to the percentage of votes, and thus know how many voters we need.

Just for kicks --

0.0049 = 1/x x = 1 / 0.0049 x = 204.08, therefore 205 voters.

.000001 % = 1/x x = 1 / .00000001 x = 100,000,000. So, 100,000,000 voters. ;-)

-
A suggestion, if you work through and see why just 1 vote for one particular candidate makes 134 voters wrong, maybe you can explain the problem to the teacher and get extra credit. :-)

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