It costs a fixed amount to hire a villa in Spain. Up to 12 people can stay in the villa. Antonio hires the villa for his family of four people. The cost per person is €300. Copy an... It costs a fixed amount to hire a villa in Spain. Up to 12 people can stay in the villa. Antonio hires the villa for his family of four people. The cost per person is €300. Copy and complete the table.
Understand the Problem
The question is asking to understand the cost structure of hiring a villa based on the number of people staying. It provides the cost for 4 people and asks to complete the cost per person for various group sizes, showing the total cost as a function of the number of people.
Answer
The completed costs per person for different group sizes are as follows: For 1 person €300, for 2 people €150, for 4 people €75, for 5 people €60, for 6 people €50, for 10 people €30, and for 12 people €25.
Answer for screen readers
| Number of people | Cost per person (€) |
|---|---|
| 4 | 75 |
| 12 | 25 |
| 2 | 150 |
| 1 | 300 |
| 6 | 50 |
| 10 | 30 |
| 5 | 60 |
Steps to Solve
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Understand the total cost for four people Antonio hires the villa for a total cost of €300 for 4 people. Thus, the total cost per person can be calculated as: $$ \text{Cost per person} = \frac{\text{Total Cost}}{\text{Number of People}} = \frac{300}{4} = 75 , \text{€} $$
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Calculate total cost for different group sizes Given that the villa has a fixed total cost, the formula for total cost remains the same irrespective of the number of people. For each group size, the total cost the villa remains €300.
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Complete the cost per person for each group size For each number of people in the table, calculate the cost per person using the formula: $$ \text{Cost per person} = \frac{300}{\text{Number of People}} $$
- For 1 person: $$ \text{Cost per person} = \frac{300}{1} = 300 , \text{€} $$
- For 2 people: $$ \text{Cost per person} = \frac{300}{2} = 150 , \text{€} $$
- For 4 people: $$ \text{Cost per person} = \frac{300}{4} = 75 , \text{€} $$
- For 5 people: $$ \text{Cost per person} = \frac{300}{5} = 60 , \text{€} $$
- For 6 people: $$ \text{Cost per person} = \frac{300}{6} = 50 , \text{€} $$
- For 10 people: $$ \text{Cost per person} = \frac{300}{10} = 30 , \text{€} $$
- For 12 people: $$ \text{Cost per person} = \frac{300}{12} = 25 , \text{€} $$
- Fill in the completed table Now fill in the values calculated into the missing spaces in the table.
| Number of people | Cost per person (€) |
|---|---|
| 4 | 75 |
| 12 | 25 |
| 2 | 150 |
| 1 | 300 |
| 6 | 50 |
| 10 | 30 |
| 5 | 60 |
More Information
The pricing structure indicates that as the number of people increases, the cost per person decreases. This is typical in rental scenarios where the total cost remains constant regardless of the number of occupants.
Tips
- Not keeping the total cost constant: Some may incorrectly believe that the total cost changes with the number of people, leading to inaccurate calculations.
- Incorrectly dividing the total cost: When calculating the cost per person, ensure that €300 is divided by the correct number of individuals, as errors in division could skew results.
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