1. **State the problem:** David is eight times older than Nicole. David's age is 32 years. We need to find Nicole's age. 2. **Define variables:** Let $a$ be Nicole's age. 3. **Write the equation:** Since David is eight times older than Nicole, we have $$32 = 8 \times a$$ 4. **Solve the equation:** Divide both sides by 8 to isolate $a$: $$a = \frac{32}{8}$$ 5. **Calculate:** $$a = 4$$ 6. **Answer:** Nicole is 4 years old. This equation models the relationship between David's and Nicole's ages and allows us to find Nicole's age by simple division.