1. **State the problem:** Solve the equation $$\frac{g}{4} + \frac{5g}{10} = \frac{9}{4}$$. 2. **Identify the formula and rules:** To solve for $g$, combine like terms and isolate $g$ on one side. 3. **Simplify the terms:** Note that $\frac{5g}{10} = \frac{g}{2}$, so the equation becomes: $$\frac{g}{4} + \frac{g}{2} = \frac{9}{4}$$ 4. **Find a common denominator for the left side:** The common denominator is 4, so rewrite: $$\frac{g}{4} + \frac{2g}{4} = \frac{9}{4}$$ 5. **Combine the fractions:** $$\frac{g + 2g}{4} = \frac{9}{4}$$ $$\frac{3g}{4} = \frac{9}{4}$$ 6. **Multiply both sides by 4 to eliminate denominators:** $$\cancel{4} \times \frac{3g}{\cancel{4}} = \cancel{4} \times \frac{9}{\cancel{4}}$$ $$3g = 9$$ 7. **Divide both sides by 3 to solve for $g$:** $$\frac{3g}{\cancel{3}} = \frac{9}{\cancel{3}}$$ $$g = 3$$ **Final answer:** $g = 3$