A shipping container will be used to transport several 120-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 14900 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 120-kilogram crates that can be loaded into the shipping container.

Question

Answer


Inequality:
xx

Answer 1

To determine the number of 120-kilogram crates that can be loaded into the shipping container, we need to take into account the maximum weight capacity of the container and the weight of the other shipments already loaded.

1. The maximum capacity of the container is 27,500 kilograms.
2. The weight of the other shipments already loaded is 14,900 kilograms.
3. Each crate weighs 120 kilograms.

We want to find \( x \), the number of crates that can be loaded without exceeding the weight limit.

First, we can calculate the remaining weight capacity of the container:

\[ \text{Remaining capacity} = 27500 - 14900 \]

Calculating this gives:

\[ \text{Remaining capacity} = 12600 \text{ kilograms} \]

Next, we need to express the total weight of the crates in relation to the remaining capacity. The weight of \( x \) crates is \( 120x \) kilograms.

Now we can set up the inequality:

\[ 120x \leq 12600 \]

To solve for \( x \), we can divide both sides by 120:

\[ x \leq \frac{12600}{120} \]

Calculating the right side:

\[ x \leq 105 \]

So the inequality that we can use to determine the number of crates is:

Inequality: \[ x \leq 105 \]

This means that a maximum of 105 crates can be loaded into the shipping container.