1. **Problem statement:** We have 50 students taking at least one of Math, Physics, Chemistry. Given: - 7 take all three subjects. - 9 take Physics and Chemistry only. - 8 take Maths and Physics only. - 5 take Maths and Chemistry only. - Let $x$ be the number taking Maths only. - $x$ take Physics only. - $x+3$ take Chemistry only. 2. **Formula and rules:** The total number of students is the sum of all disjoint groups in the Venn diagram: $$\text{Total} = \text{Maths only} + \text{Physics only} + \text{Chemistry only} + \text{Maths \& Physics only} + \text{Physics \& Chemistry only} + \text{Maths \& Chemistry only} + \text{All three}$$ 3. **Write the equation using given values:** $$50 = x + x + (x+3) + 8 + 9 + 5 + 7$$ 4. **Simplify the equation:** $$50 = 3x + 3 + 8 + 9 + 5 + 7$$ $$50 = 3x + 32$$ 5. **Solve for $x$:** $$3x = 50 - 32$$ $$3x = 18$$ $$x = 6$$ 6. **Find the number taking Chemistry only:** $$x + 3 = 6 + 3 = 9$$ **Final answers:** - $x = 6$ - Number taking Chemistry only = 9