The problem states that an airline uses a rectangular prism to hold carry-on luggage. The dimensions of the prism are given as length = 22 inches, height = 14 inches, and width = 9 inches. The suitcases are filled and weigh 0.15 pounds per cubic inch. The airline can hold 200 suitcases. We need to find the volume of one suitcase, the weight of one suitcase, and the total weight of 200 suitcases.

1. Problem Description

The problem states that an airline uses a rectangular prism to hold carry-on luggage. The dimensions of the prism are given as length = 22 inches, height = 14 inches, and width = 9 inches. The suitcases are filled and weigh 0.15 pounds per cubic inch. The airline can hold 200 suitcases. We need to find the volume of one suitcase, the weight of one suitcase, and the total weight of 200 suitcases.

2. Solution Steps

First, we calculate the volume of one suitcase (rectangular prism):

$Volume = length * height * width$

$Volume = 22 * 14 * 9$

$Volume = 2772$ cubic inches

Next, we calculate the weight of one suitcase using the given density:

$Weight = Volume * density$

$Weight = 2772 * 0.15$

$Weight = 415.8$ pounds

Finally, we calculate the total weight of 200 suitcases:

$Total\, weight = Weight\, of\, one\, suitcase * number\, of\, suitcases$

$Total\, weight = 415.8 * 200$

$Total\, weight = 83160$ pounds

3. Final Answer

Volume of 1 suitcase: 2772 cubic inches

Weight of 1 suitcase: 415.8 pounds

Weight of 200 suitcases: 83160 pounds