Question

A shipping container will be used to transport several 130-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 3100 kilograms have already been loaded into the container. Which inequality can be used to determine cc, the greatest number of 130-kilogram crates that can be loaded onto the shipping container? Answer Multiple Choice Answers 27500, is less than or equal to, 3100, plus, 130, c27500≤3100+130c 27500, is less than or equal to, 3100, c, plus, 13027500≤3100c+130 27500, is greater than or equal to, 3100, plus, 130, c27500≥3100+130c 27500, is greater than or equal to, 3100, c, plus, 13027500≥3100c+130

Answer 1

To find the inequality that represents the situation, we need to ensure that the total weight of the already-loaded shipments and the crates does not exceed the container's weight capacity of 27,500 kilograms.

Let \( c \) be the number of 130-kilogram crates. The weight of the crates can be expressed as \( 130c \) kilograms.

The total weight in the container will be the weight of the already-loaded shipments (3,100 kilograms) plus the weight of the crates \( (130c) \).

We want this total weight to be less than or equal to 27,500 kilograms. Thus, the inequality can be written as:

\[ 3100 + 130c \leq 27500 \]

Now we can check the provided options:

1. 27500 ≤ 3100 + 130c (This rearranges to the one we wrote, but is not what we need.)
2. 27500 ≤ 3100c + 130 (This is not the correct inequality.)
3. 27500 ≥ 3100 + 130c (This is the correct rearranged form of our inequality.)
4. 27500 ≥ 3100c + 130 (This is not the correct inequality.)

The correct inequality that represents the situation is:

Answer: \( 27500 \geq 3100 + 130c \)