elect 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= ?Options8: 5: 1111: 5: 89: 4: 1212: 4: 9

The problem states that (A - x): (A - y): (A - z) = 1: 7: 4 and 2A = x+y+z.

Let's solve this step by step:

Step 1: Let's assume A - x = a, A - y = b, and A - z = c. So, we have a:b:c = 1:7:4.

Step 2: From the second equation, we have A = (x+y+z)/2. Substitute the values of a, b, and c in terms of x, y, and z, we get A = (a+b+c)/2.

Step 3: Equating the two values of A, we get (x+y+z)/2 = (a+b+c)/2. Simplifying, we get x+y+z = a+b+c.

Step 4: We know that a = A - x, b = A - y, and c = A - z. Substituting these values in the equation from step 3, we get x+y+z = 3A - (x+y+z).

Step 5: Simplifying, we get 2(x+y+z) = 3A. But we know from the problem that 2A = x+y+z. Substituting this in, we get 2(2A) = 3A, which simplifies to 4A = 3A.

Step 6: This equation is not possible, which means there must be a mistake in the problem. The ratios given in the problem do not satisfy the conditions given. Therefore, none of the options provided are correct.