Constructing Simultaneous Equation for This Problem Suppose we have a rating system where a "thumbs up" equals +1 and a "thumbs down" equals - 1. We know the total number of votes cast and the current score. For example a score of +3 with 5 votes cast.

How can we determine how many "thumbs up" and "thumbs down" there are?

I imagine this would be some sort of simultaneous equation....
$x$: number of up votes

$y$: number of down votes

Now solve

$$x+y=5$$

$$x-y=3$$
Let the number thumbs up be $u$, let the total number of votes be $n$, and let the total score be $t$. Then we can say that the number of thumbs down votes must be $n-u$, so we can write:$$u-(n-u)=t$$$$\therefore 2u-n=t$$$$\therefore u=\frac{t+n}{2}$$