1. **State the problem:** Paola is twice the age of Nat. In 3 years, Paola will be 5 years older than Nat. We need to find their current ages. 2. **Define variables:** Let $N$ be Nat's current age and $P$ be Paola's current age. 3. **Write equations from the problem:** - Paola is twice Nat's age: $$P = 2N$$ - In 3 years, Paola will be 5 years older than Nat: $$P + 3 = (N + 3) + 5$$ 4. **Simplify the second equation:** $$P + 3 = N + 8$$ 5. **Substitute $P$ from the first equation into the second:** $$2N + 3 = N + 8$$ 6. **Solve for $N$:** $$2N + 3 = N + 8$$ $$2N - \cancel{N} + 3 = \cancel{N} + 8$$ $$N + 3 = 8$$ $$N = 8 - 3$$ $$N = 5$$ 7. **Find $P$ using $P = 2N$:** $$P = 2 \times 5 = 10$$ 8. **Answer:** Nat is 5 years old and Paola is 10 years old.