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To solve this problem, we need to break it down step by step.

### Information given:
- Total number of boxes: **500**
- Weight per box: **20 kg**
- Maximum load capacity of the truck: **865 kg**
- Driver's weight: **65 kg**
- Distance from factory to store (one way): **15 km**
- Fuel cost: **Rp 15,000/liter**
- Fuel consumption: **1 liter for every 10 km**

### Step-by-Step Plan:

1. **Find out how many trips are required**:
   - The truck's maximum load is **865 kg**, but we must subtract the driver’s weight (65 kg). So, the truck can carry a maximum of:
     \[
     865 \text{ kg} - 65 \text{ kg} = 800 \text{ kg}
     \]
   - Each box weighs **20 kg**, so the truck can carry:
     \[
     \frac{800}{20} = 40 \text{ boxes per trip}.
     \]
   - Total number of trips required to deliver **500 boxes**:
     \[
     \frac{500}{40} = 12.5
     \]
   - Since partial trips are not possible, it means **13 trips** will be required.

2. **Calculate the total distance for all trips**:
   - Each round trip (to and from the store) covers:
     \[
     15 \text{ km (to store)} + 15 \text{ km (return)} = 30 \text{ km}.
     \]
   - For **13 trips**, the total distance will be:
     \[
     13 \times 30 = 390 \text{ km}.
     \]

3. **Calculate the fuel needed**:
   - The truck uses **1 liter of fuel for every 10 km**. Therefore, the total fuel needed for **390 km** is:
     \[
     \frac{390}{10} = 39 \text{ liters}.
     \]

4. **Calculate the total cost of fuel**:
   - The cost of 1 liter of fuel is **Rp 15,000**. So, the total fuel cost is:
     \[
     39 \times 15,000 = Rp 585,000.
     \]

Thus, the **minimal fuel expenditure** to complete the distribution of all boxes and return to the factory is **Rp 585,000**.

---

Would you like further details or have any questions?

Here are 5 related questions to think about:
1. How would the fuel cost change if the truck's fuel efficiency was reduced to 1 liter per 8 km?
2. What would happen to the number of trips if the truck could carry 900 kg instead of 865 kg?
3

A vehicle A transporting goods will distribute 500 boxes from a factory to a store. The maximum load of the vehicle is 865 kg, and each box weighs 20 kg. The driver weighs 65 kg, and the distance from the factory to the store is 15 km. If 1 liter of gasoline costs Rp15,000 and can cover 10 km, what is the minimum cost required to distribute all boxes to the store and return the vehicle to the factory?

Discover how to calculate the minimum fuel cost for transporting 500 boxes from a factory to a store, including factors like vehicle capacity, box weight, and fuel efficiency. This problem involves algebraic and arithmetic calculations, suitable for middle school students.

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