Final answer:
Given the ratio of a to b as 6/7 and their sum as 52, we find that a is 24, b is 28, and the ratio of (a+b) to (b-a) is 13:1.
Step-by-step explanation:
The question asks to find the ratio of (a+b) to (b-a) given that the ratio of a to b is 6/7 and the sum of a and b is 52.
Let's use the given ratio a/b = 6/7. We can express a as 6x and b as 7x for some variable x. The sum of a and b is given as 52, which gives us an equation: 6x + 7x = 52. Solving this equation gives x = 4. Therefore, a = 6x = 24 and b = 7x = 28.
To find the ratio of (a+b) to (b-a), we plug in the values of a and b: (24+28) / (28-24), which simplifies to 52 / 4 = 13. Thus, the ratio of (a+b) to (b-a) is 13:1.