1. **State the problem:** Judy is $u$ years old. Her sister is 13 years old, and her brother is twice Judy's age. The total age of all three siblings is 22. 2. **Write the equation:** Let Judy's age be $u$. Then her brother's age is $2u$. The sum of their ages is: $$u + 13 + 2u = 22$$ 3. **Simplify the equation:** $$u + 13 + 2u = 22$$ $$3u + 13 = 22$$ 4. **Isolate the variable $u$:** $$3u + 13 = 22$$ $$3u = 22 - 13$$ $$3u = 9$$ 5. **Solve for $u$:** $$\cancel{3}u = \cancel{3} \times 3$$ $$u = 3$$ 6. **Answer:** Judy is 3 years old.