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Buoyancy Hot Air Balloon Question

Good evening. Here is the question I'm struggling with:

I'm really confused...
I understand that in order for the hot air balloon to 'float' the buoyant force must be equal to to the force applied by gravity (neutrally buoyant).
As the force applied by gravity is give as F = mg, we know that F = 9.81m or 9.81ϕV. This means that the buoyant force is should be -9.81m (or 9.81m in the opposite direction). The densities inside and outside is different to buoyant force should be. From there, I have no idea at all what to do....(I tried to equate things)
It'd be great if anyone could help me.
Think about the difference in mass between the cold air being excluded from volume V and the mass of the hot air that is excluding it.

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