Formulas needed:
Center of gravity = Total moment / total mass
Moment = Mass x Arm

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(1) Calculate total mass:
Total Mass = BEM + Front Seat + Aft Seat + Take-off Fuel
Total Mass = 2 635 lb + 90 lb + 186 lb + (850 lb - 230 lb) = 3 531 lb

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(2) Calculate the Moments:

• BEM = 204 793.5 in.lb
• Front Seat = 90 lb x 78 in = 7 020 in.lb
• AFT Seat = 186 lb x 117 in = 21 762 in.lb
• Take-off Fuel = 620 lb x 86 in = 53 320 in.lb

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(3) Calculate Total Moment:
Total Moment = 204 793.5 + 7 020 + 21 762 + 53 320 = 286 895.5 lb.in

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(4) Calculate CG position:
Centre of gravity = Total moment / total mass
Centre of gravity = 286 895.5 / 3 531 = 81.25 in aft of datum

Note: Question asks for Centre of gravity at take-off - Taxi fuel will be consumed before take-off, therefore is must be subtracted from our calculations.