A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 25500 kilograms. Other shipments weighing 6400 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 40-kilogram crates that can be loaded into the shipping container.

To solve the problem, we need to create an inequality that represents the situation. Let's break it down step by step.

### Information given:
- Maximum weight capacity of the container: 25,500 kg
- Other shipments already loaded: 6,400 kg
- Weight of each crate: 40 kg
- Let \( x \) represent the number of crates to be loaded.

The total weight of the other shipments and the crates must not exceed the container’s maximum capacity. The weight contributed by the crates is \( 40x \) kilograms.

So, the total weight is the sum of:
- the other shipments already loaded (6,400 kg)
- the weight of the crates (\( 40x \) kg)

Thus, the inequality to represent this is:

\[
6400 + 40x \leq 25500
\]

### Solving the inequality:

\[
40x \leq 25500 - 6400
\]

\[
40x \leq 19100
\]

Now, divide both sides by 40:

\[
x \leq \frac{19100}{40}
\]

\[
x \leq 477.5
\]

Since \( x \) represents the number of crates, and it must be a whole number, the maximum number of crates is 477.

### Conclusion:
The inequality is \( 6400 + 40x \leq 25500 \), and the maximum number of 40-kilogram crates that can be loaded into the container is **477 crates**.

Would you like more details or have any further questions? Here are some related problems to consider:

1. What if the container’s maximum weight capacity was 30,000 kg?
2. How many crates can be loaded if only 3,000 kg of other shipments were already loaded?
3. What if each crate weighed 50 kg instead of 40 kg?
4. How would the inequality change if there were two different types of crates, one weighing 30 kg and the other 40 kg?
5. What would happen if the weight capacity of the container was increased by 10%?

**Tip:** When solving word problems, always break them down into smaller steps and identify what each part represents mathematically.

A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 25500 kilograms. Other shipments weighing 6400 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine x, the number of 40-kilogram crates that can be loaded into the shipping container.

Learn how to solve the inequality 6400 + 40x ≤ 25500 to determine the maximum number of 40-kilogram crates that can be loaded into a shipping container. This problem involves key algebraic concepts, such as solving linear inequalities and step-by-step calculations. Suitable for students in Grades 6-8.

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