If (a + b)/ c = 6/5 and (b + c ) / a = 9/2 then what is the value of (a + c )/b?Options11/79/57/117/4

The problem is a system of two equations with three variables. To solve for the value of (a + c) / b, we need to manipulate the given equations to isolate (a + c) / b.

Given equations are:

1. (a + b) / c = 6/5
2. (b + c) / a = 9/2

First, let's rewrite these equations to isolate a, b, and c:

1. a + b = 6c/5
2. b + c = 9a/2

Now, we need to express a and c in terms of b.

From equation 1, we can express a as a = 6c/5 - b.

Substitute a in equation 2, we get:

b + c = 9(6c/5 - b)/2

Solving this equation for c, we get:

c = (9b + 18c - 10b) / 10

Simplify to get:

c = (b + 9c) / 5

Now, substitute c from equation 1 into this equation, we get:

b + 6c/5 = b + 9c

Solving for c, we get:

c = 5b / 3

Now, substitute c into equation 1 to get a:

a = 6(5b/3)/5 - b

Simplify to get:

a = 2b

Now, we can find the value of (a + c) / b:

(a + c) / b = (2b + 5b/3) / b

Simplify to get:

(a + c) / b = 11/3

So, the value of (a + c) / b is 11/3. But this option is not given in the question. There might be a mistake in the question or in the options provided.