To solve the problem, let's analyze the situation step by step:

Problem Breakdown:

• Total capacity of the container = 27,500 kilograms
• Weight already loaded = 7,700 kilograms
• Weight of each crate = 40 kilograms
• Let $c$ represent the number of crates to be loaded.
• The combined weight of all crates must not exceed the remaining capacity.

Setting Up the Inequality:

The total weight of the crates is represented as $40c$ because each crate weighs 40 kilograms.
The weight already in the container is 7,700 kilograms, so the inequality is:

$40c + 7700 \leq 27500$

Solving for $c$:

1. Subtract 7,700 from both sides:

$40c \leq 27500 - 7700$

$40c \leq 19800$

2. Divide both sides by 40:

$c \leq \frac{19800}{40}$

$c \leq 495$

Final Answer:

The inequality representing the total number of crates $c$ is:

$c \leq 495$

This means you can load at most 495 crates into the container.

Do you need further clarification or additional details?

Here are 5 related questions to explore further:

1. How would the inequality change if the weight already loaded increased to 10,000 kilograms?
2. What is the inequality if the container capacity changes to 30,000 kilograms?
3. How many crates could you load if the weight of each crate was 50 kilograms instead?
4. Can you set up a similar problem where the container has a maximum volume constraint?
5. What if the inequality changed to include a strict limit $<$ instead of $\leq$?

Tip: Always ensure the variables and units align correctly when solving inequalities!