1. **Problem Statement:** Among 100 students, $(75 - x)$ study physics, $(50 - x)$ study accounts, and 25 study neither. No student studies both subjects. Find $x$, the number of students studying neither, and the number studying physics and accounts. 2. **Understanding the problem:** Since no student studies both subjects, the total number studying physics or accounts is the sum of those studying physics and those studying accounts. 3. **Formula:** Total students = Students studying physics + Students studying accounts + Students studying neither. 4. **Set up the equation:** $$100 = (75 - x) + (50 - x) + 25$$ 5. **Simplify:** $$100 = 75 - x + 50 - x + 25$$ $$100 = 150 - 2x$$ 6. **Solve for $x$:** $$2x = 150 - 100$$ $$2x = 50$$ $$x = 25$$ 7. **Find the number studying physics:** $$75 - x = 75 - 25 = 50$$ 8. **Find the number studying accounts:** $$50 - x = 50 - 25 = 25$$ **Final answers:** - $x = 25$ - Number studying physics = 50 - Number studying accounts = 25