1. **State the problem:** Arthur is seven times as old as his son Nelson. Three years ago, Arthur was sixteen times as old as Nelson. We need to find their present ages. 2. **Define variables:** Let $N$ be Nelson's current age. Since Arthur is seven times Nelson's age, Arthur's current age is $7N$. 3. **Translate the condition from three years ago:** Three years ago, Nelson's age was $N - 3$ and Arthur's age was $7N - 3$. According to the problem, at that time Arthur was sixteen times Nelson's age: $$7N - 3 = 16(N - 3)$$ 4. **Solve the equation:** $$7N - 3 = 16N - 48$$ Bring all terms to one side: $$7N - 3 - 16N + 48 = 0$$ Simplify: $$-9N + 45 = 0$$ $$-9N = -45$$ $$N = \frac{-45}{-9} = 5$$ 5. **Find Arthur's age:** $$7N = 7 \times 5 = 35$$ 6. **Answer:** Nelson is 5 years old and Arthur is 35 years old now.