Balloon-assisted rocket launches
I see here a NASA balloon lifted a 2-ton scientific payload to 38km. If someone totally uninterested in CATS just wanted to win the X-Prize, what's the minimum needed in terms of launch mass (fuel tanks, propellants, engines/motors etc) to lift a 3-man capsule to a similar altitude and then ignite a rocket stage just powerful enough to rise to 100km? It'd be more than 2 tons in total, but how much more?