TITLE: Solving an inequality with the floor operator
QUESTION [1 upvotes]: Assume that $A$, $B$, $C$ are positive real numbers and that $I$ is a positive integer. How could I isolate $A$ in the inequality $\left \lfloor{AB/C}\right \rfloor \geq I$ ? The best I could do:
\begin{equation}
AB/C -1 \geq I \Rightarrow \left \lfloor{AB/C}\right \rfloor \geq I
\end{equation}
Thus, $A\geq C(1+I)/B$ is a sufficient condition for $\left \lfloor{AB/C}\right \rfloor \geq I$.

REPLY [4 votes]: $$\left\lfloor\frac{AB}{C}\right\rfloor \ge I$$
$$\implies \frac{AB}{C} \ge I$$
$$\implies A \ge \frac{IC}{B}$$
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