$$ \begin{aligned} 16000 &= 47000 \cdot \frac{a}{a+47000}&& \text{multiply ALL terms by } \color{blue}{ a+47000 }. \\[1 em](a+47000)\cdot16000 &= (a+47000)\cdot47000 \cdot \frac{a}{a+47000}&& \text{cancel out the denominators} \\[1 em]16000a+752000000 &= 47000a&& \text{move the $ \color{blue}{ 47000a } $ to the left side and $ \color{blue}{ 752000000 }$ to the right} \\[1 em]16000a-47000a &= -752000000&& \text{simplify left side} \\[1 em]-31000a &= -752000000&& \text{ divide both sides by $ -31000 $ } \\[1 em]a &= \frac{-752000000}{-31000}&& \\[1 em]a &= \frac{752000}{31}&& \\[1 em] \end{aligned} $$

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