1. Let's denote Fanny's age as $x$ years. 2. Since Fanny is younger than her uncle by 16 years, the uncle's age is $x + 16$ years. 3. The problem states that the product of their ages is exactly 15 times the sum of their ages. We can write this as an equation: $$x(x + 16) = 15(x + x + 16)$$ 4. Simplify the right side: $$x(x + 16) = 15(2x + 16)$$ 5. Expand both sides: $$x^2 + 16x = 30x + 240$$ 6. Bring all terms to one side to form a quadratic equation: $$x^2 + 16x - 30x - 240 = 0$$ $$x^2 - 14x - 240 = 0$$ 7. Solve the quadratic equation using the quadratic formula: $$x = \frac{14 \pm \sqrt{(-14)^2 - 4 \times 1 \times (-240)}}{2}$$ $$x = \frac{14 \pm \sqrt{196 + 960}}{2}$$ $$x = \frac{14 \pm \sqrt{1156}}{2}$$ $$x = \frac{14 \pm 34}{2}$$ 8. Calculate the two possible values for $x$: - $$x = \frac{14 + 34}{2} = \frac{48}{2} = 24$$ - $$x = \frac{14 - 34}{2} = \frac{-20}{2} = -10$$ 9. Since age cannot be negative, we discard $x = -10$. **Final answer:** Fanny is currently **24 years old**.