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 24500 kilograms. Other shipments weighing 13100 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.

Answer 1

To determine the number of 40-kilogram crates (denoted as \( x \)) that can be loaded into the shipping container, we can set up an inequality based on the total weight limits.

1. Identify the variables:

   • Weight of each crate = 40 kg
   • Already loaded weight = 13100 kg
   • Maximum weight limit of the container = 24500 kg

2. Write the inequality: The total weight in the container (the weight of the already loaded shipment plus the weight of the crates) should not exceed the maximum weight limit: \[ 13100 + 40x \leq 24500 \]

3. Solve the inequality:

   • Subtract 13100 from both sides: \[ 40x \leq 24500 - 13100 \] \[ 40x \leq 11400 \]
   • Now, divide both sides by 40: \[ x \leq \frac{11400}{40} \] \[ x \leq 285 \]

So, the solution to the inequality indicates that you can load at most \( x \leq 285 \) crates into the shipping container. Therefore, the number of 40-kilogram crates that can be loaded into the shipping container is at most 285 crates.