I hope someone may be able to help me solve the following equation for $y$?
$$x=\frac b{50}\left\lfloor{50ay\over b}\right\rfloor$$
I'm trying to isolate $y$ so I can program an Excel file to solve the problem when $a$, $b$, and $x$ are known values. Is there a way to express the formula in a way that can be relied upon with utilizing the "goal seeker" feature on each dataset. I have nearly $3000$ of these.
The equation $$x=\frac{1}{50} b \operatorname{floor}(50ay/b)$$ is equivalent to $$\frac{50x}{b} = \operatorname{floor}\left( \frac{50ay}{b} \right)$$ so, if $\frac{50x}{b}$ is not an integer, we have to stop, since the equation is impossible (no value of $y$ will satisfy that equation).
In the case that this is an integer, we can go on: the last equation is equivalent to $$\frac{50x}{b} \le \frac{50ay}{b} < \frac{50x}{b} +1$$ since $\frac{50a}{b} > 0$, we can divide everything by $\frac{50a}{b}$ getting $$\frac{x}{a} \le y < \frac{x}{a} + \frac{b}{50a}$$ So every number in the interval $\left[ \frac{x}{a} , \frac{x}{a}+ \frac{b}{50a} \right)$ may be a correct value for $y$.