1. **Problem statement:** We are given two true statements about visitor numbers at a swimming pool and asked to verify them mathematically. 2. **First statement:** "Die Spannweite der Besucherzahlen in der ersten Ferienwoche beträgt 150 Besucher." The range (Spannweite) is calculated as the difference between the maximum and minimum visitor numbers. Given: Maximum visitors = 286, Minimum visitors = 136 Formula: $$\text{Range} = \text{Max} - \text{Min}$$ Calculation: $$286 - 136 = 150$$ This confirms the first statement. 3. **Second statement:** "Am Sonntag kamen ein Drittel mehr Besucher als am Mittwoch." Let the number of visitors on Wednesday be $W$. Then visitors on Sunday = $W + \frac{1}{3}W = \frac{4}{3}W$ This means Sunday visitors are one third more than Wednesday visitors. 4. **Additional information:** "Am Wochenende kamen 520 Besucher in das Schwimmbad." Let Saturday visitors be $S$, Sunday visitors be $Su$. We have: $$S + Su = 520$$ Using the relation from step 3: $$Su = \frac{4}{3}W$$ Assuming Wednesday visitors $W$ equal Saturday visitors $S$ (if not given, we cannot solve further here). 5. **Part e) Problem statement:** The operator claims: "If $x$ more visitors had come on the weekend, the revenue would have been 7920." Given: - Weekend visitors = 520 - Ticket price per person = 12 6. **Formulate the equation:** Revenue with $x$ more visitors: $$12 \times (520 + x) = 7920$$ 7. **Solve for $x$:** $$12 \times (520 + x) = 7920$$ $$\Rightarrow 520 + x = \frac{7920}{12}$$ $$\Rightarrow 520 + x = 660$$ $$\Rightarrow x = 660 - 520$$ $$\Rightarrow x = 140$$ **Final answer:** - The range of visitors is 150, confirmed by calculation. - Sunday visitors are one third more than Wednesday visitors, expressed as $Su = \frac{4}{3}W$. - The number of missing visitors $x$ to reach 7920 revenue is 140.