Answer: 108

Solution:

After the eating, $444 - 5 - 9 - 25 = 405$ peanuts remain, and the three amounts form an arithmetic progression, so the middle amount, Betty's, is $\frac{405}{3} = 135.$ Hence Betty started with $135 + 9 = 144$ peanuts.

The starting amounts form a geometric progression, so they are $\frac{144}{r},$ $144,$ and $144r$ with $r \gt 1$ (Charlie had the most and Alex the least). Then $$\frac{144}{r} + 144 + 144r = 444,$$ which simplifies to $12r^2 - 25r + 12 = 0,$ with roots $r = \frac{4}{3}$ and $r = \frac{3}{4};$ since $r \gt 1,$ we take $r = \frac{4}{3}.$

So Alex initially had $144 \cdot \frac{3}{4} = 108$ peanuts. (Check: after eating, the amounts $103,$ $135,$ $167$ increase by $32$ each.)