1. **State the problem:** Solve the equation $0.10x + 0.20y = 0.19(x + y)$ for $y$ in terms of $x$. 2. **Write the equation:** $$0.10x + 0.20y = 0.19x + 0.19y$$ 3. **Group like terms:** Move all terms involving $x$ and $y$ to one side: $$0.10x - 0.19x + 0.20y - 0.19y = 0$$ 4. **Simplify coefficients:** $$-0.09x + 0.01y = 0$$ 5. **Isolate $y$:** Add $0.09x$ to both sides: $$0.01y = 0.09x$$ Divide both sides by $0.01$: $$y = \frac{0.09}{0.01}x = 9x$$ 6. **Interpretation:** The solution shows that $y$ is directly proportional to $x$ with a factor of 9. **Final answer:** $$y = 9x$$