1. The problem involves understanding ratios, formulas, and their solutions. 2. A ratio is a comparison of two quantities expressed as $a:b$ or $\frac{a}{b}$. 3. To solve problems involving ratios, set up an equation based on the given ratio and the total or other conditions. 4. For example, if the ratio of $x$ to $y$ is $3:4$ and their sum is $21$, then: $$\frac{x}{y} = \frac{3}{4}$$ $$x + y = 21$$ 5. From the ratio, express $x$ as $x = \frac{3}{4}y$. 6. Substitute into the sum equation: $$\frac{3}{4}y + y = 21$$ 7. Combine like terms: $$\frac{3}{4}y + \frac{4}{4}y = \frac{7}{4}y = 21$$ 8. Solve for $y$: $$y = \frac{21 \times 4}{7} = 12$$ 9. Find $x$: $$x = \frac{3}{4} \times 12 = 9$$ 10. Therefore, the solution is $x=9$ and $y=12$. This method applies generally to ratio problems by setting variables proportional to the ratio and using given conditions to solve.