To determine the greatest number of 50-kilogram crates that can be loaded onto the shipping container, we need to establish a relationship between the total weight in the container and its maximum capacity.
- Let \( z \) represent the number of 50-kilogram crates that can be added.
- The weight of the crates is \( 50z \) kilograms.
- The weight already loaded into the container is \( 6900 \) kilograms.
- The maximum weight that can be accommodated in the container is \( 25000 \) kilograms.
The total weight in the container, therefore, can be expressed as:
\[ 6900 + 50z \]
We want this total weight to be less than or equal to the maximum capacity of the container (25000 kg). This gives us the inequality:
\[ 6900 + 50z \leq 25000 \]
Now, rearranging the inequality to isolate \( z \):
\[ 50z \leq 25000 - 6900 \]
\[ 50z \leq 18100 \]
Dividing by 50:
\[ z \leq \frac{18100}{50} \]
Thus, the inequality that represents the situation is:
\[ 6900 + 50z \leq 25000 \]
In terms of the options provided, the correct option that expresses this situation is:
50(6900 + z) ≤ 25000
However, if we take into consideration the specific wording around \( z \) (where \( z \) is the number of crates), the clear relationship should rather be expressed directly with respect to \( z \):
25000 ≥ (6900 + 50z)
If we had to choose from the provided options, the correct inequality that directly accounts for the maximum weight with the outlined context is:
25000 ≥ 50z + 6900
3 answers