1. **Stating the problem:** We are given the ages of three people: you (9 years), your elder sister (14.5 years), and your mother who is 31.5 years older than you. We need to find: a) Your mother's age. b) The total of your ages. 2. **Formula and explanation:** To find your mother's age, we add the difference in age to your age: $$\text{Mother's age} = \text{Your age} + 31.5$$ To find the total age, we sum all three ages: $$\text{Total age} = \text{Your age} + \text{Sister's age} + \text{Mother's age}$$ 3. **Calculations:** a) Calculate mother's age: $$9 + 31.5 = 40.5$$ b) Calculate total age: $$9 + 14.5 + 40.5 = 64$$ 4. **Explanation:** We simply add the given numbers because age differences and totals are additive quantities. **Final answers:** a) Your mother is 40.5 years old. b) The total of your ages is 64 years.