1. **State the problem:** We have a Venn diagram representing staff members in an organization with total $S=1000$. The Male circle has regions labeled $100 + x$ (only male), $x$ (male and married), Married circle has $x$ (intersection) and $350$ (only married), and outside both circles is $2$ (neither male nor married). 2. **Given:** The male are $\frac{100}{x}$ (interpreted as ratio or relation given by user). We need to find $x$. 3. **Use the total count formula for Venn diagrams:** $$S = |Male \cup Married| + |Neither| = |Male| + |Married| - |Male \cap Married| + |Neither|$$ 4. **Express sets in terms of $x$:** - $|Male| = (100 + x) + x = 100 + 2x$ - $|Married| = x + 350 = x + 350$ - $|Male \cap Married| = x$ - $|Neither| = 2$ 5. **Plug into total:** $$1000 = (100 + 2x) + (x + 350) - x + 2$$ Simplify: $$1000 = 100 + 2x + x + 350 - x + 2 = 100 + 2x + 350 + 2 = 454 + 2x$$ 6. **Solve for $x$:** $$1000 = 454 + 2x$$ $$1000 - 454 = 2x$$ $$546 = 2x$$ $$x = \frac{546}{2} = 273$$ **Final answer:** $x = 273$