Question

A shipping container will be used to transport several 50-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 25000 kilograms. Other shipments weighing 11000 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine x

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x, the number of 50-kilogram crates that can be loaded into the shipping container.

Answer 1

`x\le 280`

Explanation:

First, we can write an inequality to show the maximum weight that can be loaded into the container. We can use the variable
`m` for this.

`m \le 25,\!000\text{ kg}`

Next, we can show what the weight inside the container will be composed of by defining
`m`.

`m = (11,\!000 + 50x) \text{ kg}`

We can see that
`m` has two components:

• 11,000 kg of weight already loaded
• 
  `x` number of 50 kg crates

We can solve for
`x` by replacing
`m` with its definition in the original inequality:

`m \le 25,\!000\text{ kg}`

↓ replacing
`m` with its definition

`11,\!000 + 50x \le 25,\!000`

↓ subtracting 11,000 from both sides

`50x \le 14,\!000`

↓ dividing both sides by 50

`\boxed{x\le 280}`