"Dennis Pogson"

(big snip here)
I would have divided the 3000watts (AC) by 120 Volts (AC), not 12 volts.

That size of inverter at 12 volts will need a nominal 25amps when drawing
max power. Add on say 15% for loss on conversion and you would be looking
at
near enough 30amps.

Personally, for that sort of current draw I would be looking for about
500A/H batteries and massive section cabling dependant on how close to the
inverter you can locate the batteries.

Dennis, Dennis, Dennis!
Please rethink your formula. We all make slight tactical errors. You
may not believe this, but even I have made mistakes!
Old Chief Lynn