Select the correct answerIf (a + b)/ c = 6/5 and (b + c ) / a = 9/2 then what is the value of (a + c )/b?

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

The given equations are:

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

First, let's isolate b in the first equation:

b = c * 6/5 - a

Now, let's substitute this into the second equation:

(c + (c * 6/5 - a)) / a = 9/2 (c + c * 6/5 - a) = 9/2 * a (11/5 * c - a) = 9/2 * a 11/5 * c = 9/2 * a + a 11/5 * c = 9/2 * a + 2/2 * a 11/5 * c = 11/2 * a c = 5/11 * 11/2 * a c = 5/2 * a

Now, let's substitute c = 5/2 * a into the first equation:

(a + b) / (5/2 * a) = 6/5 2 * (a + b) / 5 * a = 6/5 2 * (a + b) = 6 * a 2 * a + 2 * b = 6 * a 2 * b = 4 * a b = 2 * a

Finally, let's substitute b = 2 * a and c = 5/2 * a into the equation we want to find, (a + c) / b:

(a + 5/2 * a) / 2 * a = (3/2 * a) / 2 * a = 3/4

So, the value of (a + c) / b is 3/4.