Ax from the blinds

[msk]

I am playing in a generally pretty passive game, there aren't a lot
of situations which are too complex. But here is one which bothers me:

I have A3 in the BB or A7 in the SB, for instance. I see the flop free or
for one chip. The flop is something like A94r, for instance. Not too well
coordinated, maybe 2-3 other players, I am first. Since no one raised
pre-flop, the A is good for me, but I might also lose too much by playing
it too hard: I lot of these players *will* play any A.

What's a good plan once the A drops on the flop?
I have a plan which I use about 80% of the time, not sure it is good.

tia,

Mark