Uniform Distribution Ratios

Quick question about a level 4 CA question I came across... I was able to manipulate my solution to arrive at the same answer, but the solution they gave me did not seem that straightforward. I understand they are setting up the b-x/b-x ratio in order to solve for b and then substitute into b-a to solve for a... but I am at a loss in figuring out if this is actually an attribute of uniform distributions, or just another manipulation? How do they get 3b-15 and etc..?



It might just be the fact that it's been a foggy morning for me, as I feel like the reasoning is quite simple.



Thanks!

Uniform Distribution Ratios