How do I calculate this question? mass and balance
The basic equation is $Weight \cdot Arm = Moment$, which also means that $Arm = \frac{Moment}{Weight}$.That is all you need to work through these problems.

Calculate your starting moment:
$2,850\ lbs \cdot 101.67\ in = 289,759.50\ lbs/in$

After you add 400 lbs, the new Moment is:$(2,850 \cdot 101.67) + (400 \cdot 97.8) = 328,879.50\ lbs/in$

And the new total weight is:$ 2,850 + 400 = 3,250\ lbs $

This produces a new CG of:
$\frac{328,879.50}{3,250} = 101.193\ in$

The difference in CG is:
$101.193 - 101.67 = -0.477\ in$

Or, doing this all in one big equation:
$$
\frac{(2850 \cdot 101.67) + (400 \cdot 97.8)}{(2850 + 400)} - 101.67\ in = -0.477\ in
$$