Why is 4 liters multiplied by 800 km not by 50 liters?

Great question! The reason why 4 liters is multiplied by 800 km and then divided by 50 liters is because we're using a proportion to find the unknown distance. Here's a step-by-step explanation:

### Understanding Proportions
Proportions are used to solve problems where two ratios are equal. In this case, we know that:

- **50 liters of fuel** allows the truck to travel **800 km**.
- We want to find out how far the truck can travel with **4 liters of fuel**.

### Setting Up the Proportion
We set up a proportion where the ratio of fuel to distance remains constant:

\[
\frac{\text{Distance with 50 liters}}{50 \text{ liters}} = \frac{\text{Distance with 4 liters}}{4 \text{ liters}}
\]

Substituting the known values:

\[
\frac{800 \text{ km}}{50 \text{ liters}} = \frac{x \text{ km}}{4 \text{ liters}}
\]

Where \(x\) is the distance we want to find.

### Solving the Proportion
To solve for \(x\), we cross-multiply:

\[
800 \text{ km} \times 4 \text{ liters} = 50 \text{ liters} \times x \text{ km}
\]

This simplifies to:

\[
3200 \text{ km} \cdot \text{liters} = 50 \text{ liters} \times x \text{ km}
\]

Now, divide both sides by 50 liters to solve for \(x\):

\[
x = \frac{3200 \text{ km} \cdot \text{liters}}{50 \text{ liters}}
\]

\[
x = 64 \text{ km}
\]

### Why Multiply by 800 km and Not by 50 liters?
The multiplication by 800 km (the total distance covered with 50 liters) is necessary because it helps maintain the same proportion when reducing the fuel to 4 liters. We divide by 50 liters afterward to find out the corresponding distance that can be covered with the reduced amount of fuel.

In essence, the multiplication by 800 km represents scaling down the distance to match the reduced amount of fuel, and dividing by 50 liters adjusts this proportion to find the exact distance for 4 liters.

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Would you like to explore this further, or do you have any other questions? Here are some related practice questions:

1. If a truck uses 5 liters of fuel for 80 km, how far can it travel with 15 liters?
2. What if the fuel efficiency drops by 20%—how would that affect the distance covered?
3. If 100 liters of fuel covers 1200 km, what is the fuel consumption rate in liters per km?
4. How do you set up and solve a proportion problem?
5. How would you solve the problem if the question was about distance in miles instead of kilometers?

**Tip:** When working with proportions, always ensure the units on both sides of the equation match to avoid errors.

Learn how to calculate the distance a truck can travel with different amounts of fuel using proportions. This problem explores the relationship between fuel quantity and distance covered, with a step-by-step explanation and practice questions. Suitable for Grades 7-9.

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