How can Denver offer Hot Air Balloon rides? So the air density in Denver is 1.0 kg/m^3. And heated air has the density of 0.95 kg/m^3. So adding the weight of the basket and balloon I don't understand how a hot air balloon could get off the ground. In addition they boast to going 1 - 3 miles up! What am I missing here? 
 A: Given the imprecision in these numbers, that means that you can lift anywhere between 0 and 0.1 kg per m^3 of air. Per Wikipedia, a typical hot air balloon holds 2,800 m^3 of air in the envelope, so it can suspend something between 0 and 280 kg in the basket. A typical human weighs under 100kg, so you could probably lift between one and three people with a typical balloon, or more people with a larger-than-average one.
A: So I found the answer....I was not taking the final step of multiplying The difference in density between the surrounding air and the heated air and then multiplying by the envelope volume. I was just focusing on the difference and getting stuck there. I chose Denver because it's a mile above sea level with a known air density. I could have chosen Mt Everest with a density of 0.5 just as easily. So anyway the answer to my question was the Net Buoyancy Force Equation. Sorry if that was obvious to all of you but these concepts don't come naturally to me :)
Thank you for your time
A: There's no uniform density of heated air. It depends on the temperature (higher T -> lower density) but also on the ambient air pressure.
In Denver, cold air is less dense, because the ambient pressure is lower. But this same effect also increases the density of hot air, by the same percentage.
So, the result is that the lift of a balloon decreases with ambient pressure. Assuming the balloon itself doesn't change weight, the net paylod weight decreases even more. But the payload still can be positive if the balloon's lift exceeds the balloon's weight.
