$$ \begin{aligned} 50+100+\frac{9}{10}y &= y&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot50+10\cdot100+10 \cdot \frac{9}{10}y &= 10y&& \text{cancel out the denominators} \\[1 em]500+1000+9y &= 10y&& \text{simplify left side} \\[1 em]9y+1500 &= 10y&& \text{move the $ \color{blue}{ 10y } $ to the left side and $ \color{blue}{ 1500 }$ to the right} \\[1 em]9y-10y &= -1500&& \text{simplify left side} \\[1 em]-y &= -1500&& \text{switch signs on both sides} \\[1 em]y &= 1500&& \\[1 em] \end{aligned} $$

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