1. **State the problem:** We are given two positive integers $x$ and $y$ such that $x > y$ and the equation $x + xy = 247$. We need to find the value of $x + y$. 2. **Rewrite the equation:** The equation can be factored by factoring out $x$: $$x + xy = x(1 + y) = 247$$ 3. **Analyze the factors:** Since $x$ and $y$ are positive integers, both $x$ and $1 + y$ must be positive integers and factors of 247. 4. **Factorize 247:** The prime factorization of 247 is: $$247 = 13 \times 19$$ 5. **Possible factor pairs:** The positive factor pairs of 247 are $(1, 247)$, $(13, 19)$, and $(19, 13)$, $(247, 1)$. 6. **Assign factors to $x$ and $1 + y$:** Since $x(1 + y) = 247$ and $x > y$, we test each pair: - If $x = 13$, then $1 + y = 19 \Rightarrow y = 18$ and $x > y$ is false (13 > 18 is false). - If $x = 19$, then $1 + y = 13 \Rightarrow y = 12$ and $x > y$ is true (19 > 12). 7. **Calculate $x + y$:** $$x + y = 19 + 12 = 31$$ **Final answer:** $$\boxed{31}$$