1. **Problem statement:** You travel a base distance of 500 km for a round trip (aller-retour), but each additional friend adds 10 km to the trip. The car consumes 15 L of fuel per 100 km, and fuel costs 2 per liter. You want to find the function for the cost per person when splitting the gas cost among up to 5 people (including you). 2. **Define variables:** - Let $x$ be the total number of people (including you), where $1 \leq x \leq 5$. - Base one-way distance: 500 km. - Additional distance per friend: 10 km. - Total trip distance (round trip): $$D(x) = 2 \times (500 + 10 \times (x - 1))$$ 3. **Fuel consumption formula:** - Fuel consumption rate: 15 L per 100 km. - Total fuel used: $$F(x) = \frac{15}{100} \times D(x) = 0.15 \times D(x)$$ 4. **Total fuel cost:** - Fuel price per liter: 2. - Total cost: $$C(x) = 2 \times F(x) = 2 \times 0.15 \times D(x) = 0.3 \times D(x)$$ 5. **Cost per person:** - Split cost among $x$ people: $$\text{Cost per person} = \frac{C(x)}{x} = \frac{0.3 \times D(x)}{x} = \frac{0.3 \times 2 \times (500 + 10(x-1))}{x} = \frac{0.6 \times (500 + 10(x-1))}{x}$$ 6. **Simplify inside the parentheses:** $$500 + 10(x-1) = 500 + 10x - 10 = 490 + 10x$$ 7. **Final function:** $$\boxed{f(x) = \frac{0.6 \times (490 + 10x)}{x} = \frac{294 + 6x}{x}}$$ This function gives the cost per person for $x$ people on the round trip, considering the added distance per friend and splitting the fuel cost equally. **Note:** $x$ must be an integer between 1 and 5 inclusive.