Final answer:
To find out how many containers can fit on a 24-inch long shelf, we divide the shelf length by the longer side of the container's face. With each container having a face of 4.5 inches, approximately 5 containers can fit on the shelf side by side.
Step-by-step explanation:
The student's question pertains to the calculation of the capacity to place identical rectangular-prism containers on a shelf based on the given dimensions and the total volume of three such containers.
We know from the problem that each container has a face measuring 4.5 inches by 2 inches, and together the three containers have a total volume of 135 cubic inches.
To determine the volume of a single container, we would divide the total volume by 3, which gives us 45 cubic inches per container.
However, since the question asks how many containers can fit on a shelf that is 24 inches long, we must align the containers by the face that looks 4.5 inches by 2 inches.
As the longer side of that face is 4.5 inches, we can divide the length of the shelf by 4.5 inches to find out how many containers can sit side by side on the shelf.
This results in ≈ 5.33, which means that only 5 containers can be placed side by side on the shelf because we cannot place a fraction of a container.