1. **Problem (a):** When the sum of $2a$ and 15 is divided by 7, the result is 11. Find the value of $a$. 2. **Formula and rules:** The problem states: $$\frac{2a + 15}{7} = 11$$ To solve for $a$, multiply both sides by 7 to eliminate the denominator. 3. **Step-by-step solution:** 1. Multiply both sides by 7: $$2a + 15 = 11 \times 7$$ $$2a + 15 = 77$$ 2. Subtract 15 from both sides: $$2a = 77 - 15$$ $$2a = 62$$ 3. Divide both sides by 2: $$a = \frac{62}{2}$$ Show cancellation: $$a = \frac{\cancel{62}}{\cancel{2}} = 31$$ 4. **Answer:** $$\boxed{31}$$ This means the value of $a$ is 31.