[77newell]

Given that the AC will use about 15 amps when the compressor is running, that would be 150 amps at the batteries before adding in the losses for the inverter. You could easily have around 170 amps coming out of the batteries for this use. And as Forest said there are other uses. Having the batteries load tested would provide useful information regarding battery status though I don't see in the current information a compelling picture that the batteries are bad.