Maths/Stats challenge - 1 of 2 - polls

[EdS2]

Here's a challenge. I think it's a bit like finding fractional approximations to arbitrary numbers, but different.

Given a poll result, come up with a series of ever-better approximations of how many votes might have been cast.

For example, a poll with
A: 10%
B: 20%
C: 40%
D: 30%
could plausibly have had 10 voters. In this case there's no point going further, but in any case there's a sensible limit of 100 voters for a given result.

Here's a real-world poll result:
A: 23%
B: 41%
C: 36%

And here's another real-world result:
A: 12%
B: 18%
C: 45%
D: 25%

Two more examples from the wild:
16, 2, 51, 31
45, 17, 25, 13, 0

(All of those have answers which are below 100)

(We should perhaps assume that percentages have been rounded, so we might get an approximate and not exact match.)