$$ \begin{aligned} 16000 &= 47000 \cdot \frac{r}{47000}+r&& \text{multiply ALL terms by } \color{blue}{ 47000 }. \\[1 em]47000\cdot16000 &= 47000\cdot47000 \cdot \frac{r}{47000}+47000r&& \text{cancel out the denominators} \\[1 em]752000000 &= 47000r+47000r&& \text{simplify right side} \\[1 em]752000000 &= 94000r&& \text{ swap the left and right side of the equation } \\[1 em]94000r &= 752000000&& \text{ divide both sides by $ 94000 $ } \\[1 em]r &= \frac{752000000}{94000}&& \\[1 em]r &= 8000&& \\[1 em] \end{aligned} $$

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