1. **State the problem:** We have 80 students in total. - 9 students study both French and German. - 35 students study only French. - 2 students study neither French nor German. We need to find how many students study only German. 2. **Set up the Venn diagram variables:** Let: - $x$ = number of students who study only German. - Given: students who study both French and German = 9. - Students who study only French = 35. - Students who study neither = 2. 3. **Write the total students equation:** Total students = students only French + students only German + students both + students neither $$80 = 35 + x + 9 + 2$$ 4. **Simplify the equation:** $$80 = 35 + 9 + 2 + x$$ $$80 = 46 + x$$ 5. **Solve for $x$:** $$x = 80 - 46$$ $$x = 34$$ 6. **Answer:** The number of students who study only German is **34**. This completes the Venn diagram: - Only French: 35 - Only German: 34 - Both French and German: 9 - Neither: 2