4. A car rental shop offers a car rental for 3 days for 150 euros. This is a gasoline car and it takes5
liters of gasoline per 100 km. The gasoline price is 1,8 euros per liter. A group of 5 students are
planning to rent this car to make a weekend trip to a city with a total distance of 1200 km. The
other option is to buy train tickets: the tickets, without a discount, which is 30 % for students,

O202 are 130 euros per person for a two-way ticket.

a) How much is the difference in price for the transportation per student for these 2
options?

b) If the students were only two, how much would the difference be then?
c) If you travel by yourself, how much is the price of a train ticket of the price of this car

trip (including rental and gasoline)?

Let's break down the problem and solve each part step by step.

### Part A: Difference in price per student for the two transportation options (5 students)

1. **Car Rental Option:**
   - **Rental Cost:** 150 euros for 3 days.
   - **Gasoline Consumption:** 5 liters per 100 km.
   - **Total Distance:** 1200 km.
   - **Gasoline Price:** 1.8 euros per liter.

   **Total Gasoline Consumption:**
   \[
   \text{Total gasoline needed} = \left(\frac{5 \text{ liters}}{100 \text{ km}}\right) \times 1200 \text{ km} = 60 \text{ liters}
   \]

   **Total Gasoline Cost:**
   \[
   \text{Total gasoline cost} = 60 \text{ liters} \times 1.8 \text{ euros/liter} = 108 \text{ euros}
   \]

   **Total Cost for Car Trip:**
   \[
   \text{Total cost} = \text{Rental cost} + \text{Gasoline cost} = 150 \text{ euros} + 108 \text{ euros} = 258 \text{ euros}
   \]

   **Cost Per Student:**
   \[
   \text{Cost per student} = \frac{258 \text{ euros}}{5 \text{ students}} = 51.6 \text{ euros}
   \]

2. **Train Ticket Option:**
   - **Original Ticket Price:** 130 euros per person (two-way).
   - **Student Discount:** 30%.

   **Discounted Ticket Price:**
   \[
   \text{Discounted price} = 130 \text{ euros} \times (1 - 0.3) = 130 \text{ euros} \times 0.7 = 91 \text{ euros per person}
   \]

   **Difference in Price per Student:**
   \[
   \text{Difference} = 91 \text{ euros} - 51.6 \text{ euros} = 39.4 \text{ euros}
   \]

   **Answer for Part A:**
   \[
   \text{Difference in price per student} = 39.4 \text{ euros}
   \]

### Part B: Difference in price per student for the two transportation options (2 students)

1. **Cost Per Student for the Car Option (2 students):**
   \[
   \text{Cost per student} = \frac{258 \text{ euros}}{2 \text{ students}} = 129 \text{ euros}
   \]

2. **Difference in Price per Student:**
   \[
   \text{Difference} = 129 \text{ euros} - 91 \text{ euros} = 38 \text{ euros}
   \]

   **Answer for Part B:**
   \[
   \text{Difference in price per student} = 38 \text{ euros}
   \]

### Part C: Price of a train ticket vs. price of a car trip (1 student)

1. **Cost Per Student for the Car Option (1 student):**
   \[
   \text{Cost per student} = \frac{258 \text{ euros}}{1 \text{ student}} = 258 \text{ euros}
   \]

2. **Difference in Price:**
   \[
   \text{Difference} = 258 \text{ euros} - 91 \text{ euros} = 167 \text{ euros}
   \]

   **Answer for Part C:**
   \[
   \text{Difference in price for one student} = 167 \text{ euros}
   \]

### Summary of Answers:
- **Part A:** 39.4 euros difference per student (5 students).
- **Part B:** 38 euros difference per student (2 students).
- **Part C:** 167 euros difference (1 student).

Would you like to dive deeper into any specific part or have further questions?

### Follow-Up Questions:
1. How would the cost per student change if the gasoline price increased by 10%?
2. What if the car rental price was discounted by 15% for students?
3. How much would the total car trip cost if the distance was 1500 km instead of 1200 km?
4. What is the cost difference if the students took an additional trip of 200 km during the weekend?
5. How much would each student save if there was a group discount of 10% on the train tickets?

### Tip:
When comparing travel options, always consider both fixed costs (like rental fees) and variable costs (like fuel), as these can significantly impact the overall price per person, especially when group sizes change.

Calculate the cost difference per student between renting a car for a weekend trip and buying train tickets. Includes detailed calculations for car rental fees, gasoline costs, train ticket prices, and student discounts. Suitable for advanced high school students studying cost comparison and percentage calculations.

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