$$ \begin{aligned} z+z\cdot\frac{5}{100} &= 1050&& \text{multiply ALL terms by } \color{blue}{ 100 }. \\[1 em]100z+100z\cdot\frac{5}{100} &= 100\cdot1050&& \text{cancel out the denominators} \\[1 em]100z+5z &= 105000&& \text{simplify left side} \\[1 em]105z &= 105000&& \text{ divide both sides by $ 105 $ } \\[1 em]z &= \frac{105000}{105}&& \\[1 em]z &= 1000&& \\[1 em] \end{aligned} $$

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