The first calculation is simple enough to derive and is one of a number of ways of expressing the CG .. not one which I would use, but that is not relevant to the discussion, I guess.
The second appears to me to be so much arrant nonsense .. wherever did you come across it ? And, if you could be so kind to advise the answer .. did the person or book whence it came suggest any practical use for it ?
However, if one wanted to express the CG in %MAC values using this format, it is easy enough to derive the components by substituting the CG expression from the first post into the standard %MAC equation ... and then juggling the bits around a tad to come up with the required layout .. (careless mistakes on my part excepted ..)
LEMAC = distance from datum to leading edge of the MAC
MAC = length of the MAC
remainder as per the first post ...
%MAC = 100(CG - LEMAC)/MAC
= (100Wa - 100bRA - 100WLEMAC)/WMAC
= 100/MAC*(a - LEMAC) - 100b/MAC*RA/W
hence
c = 100/MAC*(a - LEMAC)
d = 100b/MAC
.... but who in their right senses would want to do such an apparently strange sort of thing ? My tiny little mind is reeling just from the suggestion ...
.. or have I missed something fundamental to weight control over the past 40-odd years ?
I see that MFS has responded at the same time ... might just as well leave both posts up, I guess.