The question is solved in the best possible manner. I dont see any problem with it.
Kindly state which part you are not able to understand.

I agree with you that a lot of problems aren't explained in the best/quickest/easiest way. That is because the Official Guide always gives the "official" explanation, where there may be some shortcut or other strategy you can apply to solve the problem more efficiently. The GMAC isn't in the business of giving away GMAT tricks, so it's not surprising that the Official Guide is "by the book".

That's why it's so important to get a prep book or take a prep class and apply what you learned to the OG, carefully analyzing every problem in terms of the tricks etc. that you learned in your book/class.

For example, in the problem you reference, there's nothing wrong per se with the way the OG explains it. However, maybe a faster way is to plug in numbers for the variables.

Hope this helps!