Which inequality represents all possible values of x, the number of boxes that can be loaded into the Amazon truck?

Understand the Problem

The question asks which inequality correctly represents the maximum weight capacity of an Amazon truck given a weight bench and boxes. We need to account for the weight of the bench and the boxes in relation to the truck's weight limit.

Answer

The inequality is $25x + 600 \leq 2100$.

Steps to Solve

Identify the total weight limitation

The total weight capacity of the truck is $2,100$ pounds.

Account for the weight of the bench

The weight of the bench is $600$ pounds. This means the remaining weight capacity for the boxes can be calculated as:

$$ 2100 - 600 = 1500 $$

Define the weight of the boxes

Each box weighs $25$ pounds. If we let $x$ represent the number of boxes, the total weight of the boxes is expressed as:

$$ 25x $$

Set up the inequality

To find the maximum number of boxes that can be loaded without exceeding the total weight capacity, we establish the inequality:

$$ 600 + 25x \leq 2100 $$

Rearrange the inequality

Moving the $600$ to the other side gives us:

$$ 25x \leq 2100 - 600 $$
$$ 25x \leq 1500 $$

The correct inequality that represents all possible values of $x$ is:

$$ 25x + 600 \leq 2100 $$

More Information

This inequality illustrates that the combined weight of the weight bench and the boxes should not exceed the truck's maximum carrying capacity. By solving this inequality, one can determine the maximum number of boxes that can be loaded without exceeding the limit.

Tips

Ignoring the weight of the bench: Some may add only the weight of boxes without considering the weight of the bench. Always account for all weights in the total capacity.
Misinterpreting the inequality: Confusing the direction of the inequality (using $<$ instead of $\leq$) can lead to incorrect conclusions.

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