The ratio of the area of Rectangle A to the shaded area of Rectangle A is 7 : 2. The ratio of the area of Rectangle B to the unshaded area of Rectangle B is 5 : 2.Find the ratio of the unshaded area of Rectangle A to the area of the whole figure.

To solve this problem, we need to break it down into several steps:

Step 1: Understand the problem The problem gives us two ratios. The first ratio tells us that the area of Rectangle A to the shaded area of Rectangle A is 7:2. This means that for every 7 parts of Rectangle A, 2 parts are shaded. The second ratio tells us that the area of Rectangle B to the unshaded area of Rectangle B is 5:2. This means that for every 5 parts of Rectangle B, 2 parts are unshaded.

Step 2: Find the unshaded area of Rectangle A Since the ratio of the area of Rectangle A to the shaded area of Rectangle A is 7:2, this means that the unshaded area of Rectangle A is 7 - 2 = 5 parts.

Step 3: Find the total area of the figure The total area of the figure is the sum of the areas of Rectangle A and Rectangle B. Since the ratio of the area of Rectangle A to the shaded area of Rectangle A is 7:2, the total area of Rectangle A is 7 parts. Since the ratio of the area of Rectangle B to the unshaded area of Rectangle B is 5:2, the total area of Rectangle B is 5 parts. Therefore, the total area of the figure is 7 + 5 = 12 parts.

Step 4: Find the ratio of the unshaded area of Rectangle A to the area of the whole figure The unshaded area of Rectangle A is 5 parts and the total area of the figure is 12 parts. Therefore, the ratio of the unshaded area of Rectangle A to the area of the whole figure is 5:12.