1. **State the problem:** Simplify the expression $$7q + 9r + \frac{3q + 10r}{5}$$. 2. **Understand the expression:** The expression consists of two parts: the sum of terms $7q + 9r$ and the fraction $\frac{3q + 10r}{5}$. 3. **Find a common denominator:** To combine the terms, express $7q + 9r$ as a fraction with denominator 5: $$7q + 9r = \frac{5(7q + 9r)}{5} = \frac{35q + 45r}{5}$$ 4. **Add the fractions:** Now add the two fractions: $$\frac{35q + 45r}{5} + \frac{3q + 10r}{5} = \frac{(35q + 45r) + (3q + 10r)}{5}$$ 5. **Combine like terms in the numerator:** $$35q + 3q = 38q$$ $$45r + 10r = 55r$$ So the numerator becomes: $$38q + 55r$$ 6. **Write the simplified expression:** $$\frac{38q + 55r}{5}$$ **Final answer:** $$\frac{38q + 55r}{5}$$