Christine owns an aquarium which is 24 inches long, 12 inches wide, and 13 inches tall. After placing an artificial coral reef, the height of the water change from 9 inches to 12 inches. What is the ratio of the volume of water before placing the artificial coral reef to the volume of the artificial coral reef?

To solve this problem, we first need to calculate the volume of the water before and after the artificial coral reef is placed in the aquarium.

Step 1: Calculate the volume of the water before the artificial coral reef is placed. The volume (V) of a rectangular prism (like our aquarium) is calculated by multiplying the length (l), width (w), and height (h). So, V = lwh. Before the coral reef is placed, the height of the water is 9 inches. So, the volume of the water is V = 24 inches * 12 inches * 9 inches = 2592 cubic inches.

Step 2: Calculate the volume of the water after the artificial coral reef is placed. After the coral reef is placed, the height of the water is 12 inches. So, the volume of the water is V = 24 inches * 12 inches * 12 inches = 3456 cubic inches.

Step 3: Calculate the volume of the artificial coral reef. The volume of the coral reef is the difference between the volume of the water after the coral reef is placed and the volume of the water before the coral reef is placed. So, the volume of the coral reef is 3456 cubic inches - 2592 cubic inches = 864 cubic inches.

Step 4: Calculate the ratio of the volume of the water before the coral reef is placed to the volume of the coral reef. The ratio is 2592 : 864, which simplifies to 3:1 when we divide both numbers by 864.

So, the ratio of the volume of the water before placing the artificial coral reef to the volume of the artificial coral reef is 3:1.