1. **State the problem:** Solve the equation $$\frac{p}{2} + \frac{p}{3} = 10$$ for $p$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to combine terms. 3. **Find the common denominator:** The denominators are 2 and 3, so the least common denominator (LCD) is 6. 4. **Rewrite each term with denominator 6:** $$\frac{p}{2} = \frac{3p}{6}, \quad \frac{p}{3} = \frac{2p}{6}$$ 5. **Combine the fractions:** $$\frac{3p}{6} + \frac{2p}{6} = \frac{3p + 2p}{6} = \frac{5p}{6}$$ 6. **Set the equation:** $$\frac{5p}{6} = 10$$ 7. **Solve for $p$ by multiplying both sides by 6:** $$5p = 10 \times 6 = 60$$ 8. **Divide both sides by 5:** $$p = \frac{60}{5} = 12$$ **Final answer:** $p = 12$