1. **State the problem:** Kaye is currently 24 years old and her cousin Pia is 9 years old. We need to find in how many years Kaye's age will be double Pia's age. 2. **Define variables:** Let $x$ be the number of years in the future when Kaye's age is twice Pia's age. 3. **Set up the equation:** In $x$ years, Kaye's age will be $24 + x$ and Pia's age will be $9 + x$. The equation is: $$24 + x = 2(9 + x)$$ 4. **Solve the equation:** $$24 + x = 18 + 2x$$ Subtract $x$ from both sides: $$24 = 18 + x$$ Subtract 18 from both sides: $$24 - 18 = x$$ $$6 = x$$ 5. **Interpret the result:** In 6 years, Kaye will be double Pia's age. 6. **Check:** In 6 years, Kaye's age will be $24 + 6 = 30$ and Pia's age will be $9 + 6 = 15$. Indeed, $30$ is double $15$. **Final answer:** $6$ years