To determine the number of 40-kilogram crates (let's denote that number as x) that can be loaded into the shipping container, we need to set up and solve an inequality that takes into account the maximum weight capacity of the container, the weight of the already loaded shipments, and the weight of each additional crate.
Let's start with the maximum weight capacity of the container, which is 25,500 kilograms.
Other shipments already loaded weigh 11,400 kilograms.
Let's denote the weight of each new crate as w, which is 40 kilograms.
The number of new crates to be loaded is x.
The total weight of the additional x crates is the number of crates (x) times the weight of each crate (w). So the total weight for the new crates will be w * x = 40x kilograms.
Now we can set up our inequality. The weight of the other shipments plus the total weight of the additional crates must be less than or equal to the maximum weight capacity of the container:
Weight of other shipments + Weight of x crates ≤ Maximum weight capacity
11,400 + 40x ≤ 25,500
Now let's solve the inequality for x:
Subtract 11,400 from both sides:
40x ≤ 25,500 - 11,400
40x ≤ 14,100
Now divide both sides by 40 to solve for x:
x ≤ 14,100 / 40
x ≤ 352.5
Since we cannot have a fraction of a crate, we have to take the floor of the result (i.e., it has to be a whole number). The largest whole number that is less than or equal to 352.5 is 352. Therefore, the maximum number of 40-kilogram crates that can be loaded into the container is 352.
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 11400 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.
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