If (a + b)/ c = 6/5 and (b + c ) / a = 9/2 then what is the value of (a + c )/b?Options7/411/79/57/11

To solve this problem, we can use the method of substitution or elimination. Here are the steps:

1. We have two equations: (a + b)/c = 6/5 and (b + c)/a = 9/2. We can rewrite these equations as: a + b = 6c/5 and b + c = 9a/2.

2. Multiply the first equation by 5 and the second equation by 2 to get rid of the fractions: 5a + 5b = 6c and 2b + 2c = 9a.

3. Now, we can rearrange these equations to isolate 'a' in both: a = (6c - 5b)/5 and a = (2b + 2c)/9.

4. Since both expressions are equal to 'a', we can set them equal to each other and solve for 'c': (6c - 5b)/5 = (2b + 2c)/9.

5. Multiply both sides by 45 to clear the fractions: 9(6c - 5b) = 5(2b + 2c).

6. Simplify to get: 54c - 45b = 10b + 10c.

7. Rearrange to get all terms involving 'c' on one side and 'b' on the other: 44c = 55b.

8. Simplify to get: c = 55b/44 = 5b/4.

9. Substitute c = 5b/4 into the first original equation: a + b = 6(5b/4)/5 = 6b/4 = 3b/2.

10. Rearrange to get: a = 3b/2 - b = b/2.

11. Now we have a = b/2 and c = 5b/4. Substitute these into the expression we want to find: (a + c)/b = (b/2 + 5b/4) / b = 7b/4b = 7/4.

So, the value of (a + c)/b is 7/4.