1. **Problem statement:** You travel a base distance of 500 km for a round trip (aller-retour), but each additional friend you invite (up to 5 people including you) adds 10 km to the trip. 2. **Given data:** - Base distance: 500 km - Additional distance per friend: 10 km - Fuel consumption: 15 L/100 km - Fuel cost: 2 per liter - Number of people including you: $n$, where $1 \leq n \leq 5$ 3. **Goal:** Find the function $f(n)$ that gives the cost per person for the gas. 4. **Step 1: Calculate total distance for $n$ people.** - Additional distance added: $(n-1) \times 10$ km - Total one-way distance: $500 + 10(n-1)$ km - Since the trip is round trip, total distance is: $$D(n) = 2 \times \bigl(500 + 10(n-1)\bigr) = 2 \times (500 + 10n - 10) = 2 \times (490 + 10n) = 980 + 20n$$ 5. **Step 2: Calculate total fuel consumption.** - Fuel consumption rate: 15 L per 100 km - Total fuel used: $$F(n) = \frac{15}{100} \times D(n) = 0.15 \times (980 + 20n) = 147 + 3n$$ liters 6. **Step 3: Calculate total fuel cost.** - Cost per liter: 2 - Total cost: $$C(n) = 2 \times F(n) = 2 \times (147 + 3n) = 294 + 6n$$ 7. **Step 4: Calculate cost per person.** - Number of people: $n$ - Cost per person: $$f(n) = \frac{C(n)}{n} = \frac{294 + 6n}{n}$$ 8. **Step 5: Simplify the cost per person function.** $$f(n) = \frac{294}{n} + 6$$ **Final answer:** $$\boxed{f(n) = \frac{294}{n} + 6 \quad \text{for} \quad 1 \leq n \leq 5}$$ This function gives the gas cost per person depending on the number of people $n$ sharing the cost.