You don’t actually have to add “extra” air to have the cabin pressurised - just don’t let the air that was already in it on the ground escape while you ascend to 35000 ft!
However, this is oversimplifying. As DanBlather says, some of the air that was in the plane is allowed to escape as you ascend, causing the cabin pressure to fall to the equivalent of up to an 8000 ft altitude. Also, during the flight, air is allowed to escape and is replenished with pressurised air from the engine compressors, maintaining the same pressure but replacing the oxygen consumed by the passengers and removing the carbon dioxide exhaled by them.
If you read the Facts and trivia about the 747, it does indeed declare that “when pressurised, the Boeing 747 holds about a ton of air”. This doesn’t mean that an extra ton of air has been added however - in fact it implies that the 747 holds more than a ton of air when it’s sitting on the ground with its doors open.
Your question can be answered, in terms of how much more air there is in the plane when it is pressurised compared to how much there would be at 35000 ft. For an exact answer we need to know the pressurised volume of a 747, which isn’t easy to find out - for one thing, there are so many variants. But for a ballpark figure:
747-400 - passenger cabin volume is 876 cubic meters, and the cargo volume is another 150 cubic meters.
First, sitting on the ground:
The mass of a cubic meter of air at atmospheric pressure is 1.22 kg, so that implies that a 747-400 contains about 1300 kg of air, sitting on the ground with its doors open, with the air at 15 deg C.
Then you need to know the density of the comfortably warm, slightly moist air in the pressurised cabin, and the density of the very cold, dry, thin air outside it at 35000 ft.
There’s quite a few variables there, which I don’t propose to play with. For a ballpark figure we can use the pressures and assume that air behaves like an ideal gas, i.e. halving the pressure halves the density. I’m going to neglect temperature completely.
At ground level, the pressure is 760mm of Hg, and the density is 1.22 kg
At 8000ft, the pressure is 565mm of Hg, implying a density of 0.9 kg /m[sup]3[/sup]
At 35000ft, the pressure is 179mm of Hg implying a density of 0.3 kg /m[sup]3[/sup].
So the mass of air in the 747-400 pressurised to 8000 ft is about 920kg, and the mass of air in a 747-400 that has suffered a complete blowout at 35000 ft is about 308 kg. So I make the “extra” air to be in the 600kg region - closer to half a ton than a ton.
And on preview, I see that working with about half the pressurised volume I was, 1920s Style Death Ray comes up with about half my answer, which is good!