If 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= ?

To solve this problem, we need to use the concept of ratios and proportions. Here are the 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 equations.

From the first equation, we can write:

x = A - (A - x) = A - 1k (where k is a constant representing the ratio) y = A - (A - y) = A - 7k z = A - (A - z) = A - 4k

Step 4: Substituting these values in the second equation, we get:

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

Step 5: Substituting A = 12k in the equations for x, y, and z, we get:

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

Step 6: Therefore, the ratio x:y:z is 11k:5k:8k, which simplifies to 11:5:8.

So, x:y:z = 11:5:8.