Select the correct answerIf x, y, z are three positive numbers such that (A - x): (A - y): (A - z) = 1: 7: 4 and 2A = x+y+z, then x:y:z= ?

The problem can be solved in the following steps:

Step 1: We are given that (A - x): (A - y): (A - z) = 1: 7: 4. This means that A - x, A - y, and A - z are in the ratio 1:7:4.

Step 2: We are also given that 2A = x + y + z.

Step 3: We can express x, y, and z in terms of A using the given ratios.

From the first ratio, we have: x = A - 1k (where k is a constant representing the common difference in the ratio) y = A - 7k z = A - 4k

Step 4: Substitute these expressions into the second equation to solve for A:

2A = (A - 1k) + (A - 7k) + (A - 4k) 2A = 3A - 12k 12k = A

Step 5: Substitute A = 12k back into the expressions for x, y, and z:

x = 12k - 1k = 11k y = 12k - 7k = 5k z = 12k - 4k = 8k

Step 6: The ratio x:y:z is therefore 11:5:8.