To determine the greatest number of 140-kilogram crates that can be loaded into the shipping container, we first need to calculate the remaining weight capacity of the container after accounting for the already loaded shipments.
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Determine the total weight capacity of the container: \[ \text{Total weight capacity} = 28000 \text{ kg} \]
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Account for the weight of already loaded shipments: \[ \text{Weight of shipments already loaded} = 13900 \text{ kg} \]
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Calculate the remaining weight capacity: \[ \text{Remaining weight capacity} = \text{Total weight capacity} - \text{Weight of shipments already loaded} \] \[ \text{Remaining weight capacity} = 28000 \text{ kg} - 13900 \text{ kg} = 14100 \text{ kg} \]
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Determine the weight of one crate: \[ \text{Weight of one crate} = 140 \text{ kg} \]
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Calculate the greatest number of crates that can fit within the remaining weight capacity: \[ \text{Number of crates} = \frac{\text{Remaining weight capacity}}{\text{Weight of one crate}} = \frac{14100 \text{ kg}}{140 \text{ kg}} \]
Performing the division: \[ \text{Number of crates} = 100.71428571428571 \]
Since we cannot load a fraction of a crate, we round down to the nearest whole number: \[ \text{Greatest number of crates} = 100 \]
Thus, the greatest number of 140-kilogram crates that can be loaded into the shipping container is \(\boxed{100}\).
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