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I just questioned myself this:

Given that I have on a reddit post:

  • $5$ net upvotes
  • $65\%$ upvote ratio.

How many upvotes and downvotes do I have in total?.

I think its solvable, but after some math I couldn't formulate the right equations to solve it.

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    $\begingroup$ If you have $u$ upvotes, how many downvotes do you have? How many votes do you have in total? $\endgroup$ – N. F. Taussig May 17 '19 at 21:26
  • $\begingroup$ @N.F.Taussig I'm not 100% sure but I think reddit shows the net amount of upvotes you have, that means, the number "5" that shows in your upvotes/downvotes section shows the difference between them. In other words, you can have 0 net upvotes, and 1000 votes in total. $\endgroup$ – Artemix May 17 '19 at 21:40
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Let $U$ be the number of up-votes . Let $D$ be the number of down-votes.

The general idea is that when we have two statements $S(U,D)$ and $T(U,D),$ and if $S(U,D)$ is equivalent to a formula $U=f(D), $ then $S(U,D)\land T(U,D)$ implies $T(f(D),D), $ which is a statement only about $D$ and might be enough to determine a unique $D,$ and then $U $ is determined by $U=f(D).$

In this case $S(U,D)$ is $ U-D=5,$ so $U=f(D)=D+5.$ And $T(U,D)$ is $U=0.65 (U+D).$

So $S(U,D)\land T(U,D)$ implies $$(D+5)=0.65((D+5)+D).$$

BTW this implies $D=\frac {35}{6}$ and $U=\frac {65}{6}. $ If fractional votes are not allowed then there is no solution.

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  • $\begingroup$ Right, but whats most likely the answer in this case is that the real % value is 0.625 and the answer I would be looking for is 8 total votes, 5 upvotes and 3 downvotes. Which the formula described above doesn't come close to the real result. Is any way to purely mathematically solve this problem? or should I write a programming algorithm to find it? $\endgroup$ – Artemix May 17 '19 at 23:03
  • $\begingroup$ I understood "5 NET upvotes" to mean 5 more ups than downs, and "65% upvote ratio" to mean U/(U+D)=0.65, not 5/8 $\endgroup$ – DanielWainfleet May 18 '19 at 4:27
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$x$ up, $y$ down, $\frac x {x+y} =.65$, and $x-y=5$ solve two equations in two unknowns.

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  • $\begingroup$ But if I replace them it gives me 10.8 votes, which is not an integer number, I actually came up with the same result before. $\endgroup$ – Artemix May 17 '19 at 21:46
  • $\begingroup$ @Artemix I suspect what this means is that $65\%$ is the percentage rounded to the nearest integer. $\endgroup$ – N. F. Taussig May 17 '19 at 21:50
  • $\begingroup$ Yes you are right, it must be 11 votes in total then. Thanks. Btw, is there a mathematical function that represents an integer?, as in to put in a equation?. @N.F.Taussig $\endgroup$ – Artemix May 17 '19 at 22:17
  • $\begingroup$ Wait, by doing some quick tests I found out that the closest % would be 62.5 (8 total votes, 3 downvotes and 5 upvotes), which 10.8 doesn't even help me to find. $\endgroup$ – Artemix May 17 '19 at 22:24

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