1. **Problem statement:** You travel a 500 km trip, the car consumes 15 L per 100 km, and oil costs 2 per liter. You can invite up to 4 friends, but each friend adds 10 km to the trip. The trip is round-trip (aller-retour), and you want to split the gas cost among all passengers including yourself. 2. **Define variables:** Let $x$ be the number of friends you invite, where $0 \leq x \leq 4$. 3. **Calculate total distance:** The base one-way distance is 500 km. Each friend adds 10 km, so one-way distance is $500 + 10x$ km. 4. **Round-trip distance:** Since the trip is aller-retour, total distance is $$D = 2 \times (500 + 10x) = 1000 + 20x$$ km. 5. **Fuel consumption:** The car burns 15 L per 100 km, so total liters used is $$L = \frac{15}{100} \times D = \frac{15}{100} \times (1000 + 20x) = 15 \times (10 + 0.2x) = 150 + 3x$$ liters. 6. **Total cost:** Oil costs 2 per liter, so total cost is $$C = 2 \times L = 2 \times (150 + 3x) = 300 + 6x$$. 7. **Cost per person:** Total passengers are $x$ friends plus you, so $x+1$ people. Cost per person is $$\text{Cost per person} = \frac{C}{x+1} = \frac{300 + 6x}{x+1}$$. 8. **Simplify the cost per person:** $$\frac{300 + 6x}{x+1} = \frac{6(50 + x)}{x+1}$$ No further simplification is possible without specific $x$ values. **Final formula:** $$\boxed{\text{Cost per person} = \frac{300 + 6x}{x+1} \text{ where } 0 \leq x \leq 4}$$ This function gives the gas cost each person pays depending on the number of friends invited.