Assuming they are looking for the fuelled up CG as %MAC:
Ignore the stations. All you need is a distance from a datum (i e a fulcrum) and the mass. There is no requirement to convert between STA and %MAC, nor do you need to know the actual position of the datum.
Just use %MAC as your fulcrums. A %MAC is a given length from the %MAC datum, and that's all you need. Just calculate the moments as usual in the rather odd unit pound-%MAC, rather than the pound-inches, kg-inches or kg-meters which you are probably more accustomed to.
BOW: 4200 lbs * 20 %MAC = 84.000 pound-%MAC
Fuel: 500 lbs * 30 %MAC = 15.000 pound-%MAC
Sum up the mass and the moments, again as per standard procedure.
TOW: 4700 lbs, moment 99.000 pound-%MAC.
And, as always, calculate the CG in %MAC by dividing the moment by the mass:
TOW: 4700 lbs @ 99.000/4700 = 21.06 %MAC.
Last edited by ft; 25th August 2009 at 09:35.
Reason: Correcting typo(s) as pointed out by JT... twice!