Subjects algebra

Villa Cost B29B86

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1. **Stating the problem:** We want to understand how the cost per person changes when different numbers of people stay in the villa. 2. **Given information:** The villa has a fixed total cost, and up to 12 people can stay. Antonio's family of 4 pays 300 per person. 3. **Finding the total cost:** Since 4 people pay 300 each, total cost is $$4 \times 300 = 1200$$. 4. **Formula:** Total cost is fixed, so cost per person depends on number of people: $$\text{Cost per person} = \frac{\text{Total cost}}{\text{Number of people}}$$. 5. **Calculate cost per person for each number:** - For 12 people: $$\frac{1200}{12} = 100$$ - For 2 people: $$\frac{1200}{2} = 600$$ - For 1 person: $$\frac{1200}{1} = 1200$$ - For 6 people: $$\frac{1200}{6} = 200$$ - For 10 people: $$\frac{1200}{10} = 120$$ - For 5 people: $$\frac{1200}{5} = 240$$ 6. **Explanation:** The more people share the fixed total cost, the less each person pays. When fewer people stay, each pays more. 7. **Summary:** The cost per person is inversely proportional to the number of people, calculated by dividing the fixed total cost 1200 by the number of people. **Final completed table:** | Number of people | 4 | 12 | 2 | 1 | 6 | 10 | 5 | |-----------------|---|----|---|---|---|----|---| | Cost per person (€) | 300 | 100 | 600 | 1200 | 200 | 120 | 240 |