Okay.... will try and answer in parts... however the solution entirely depends on the followings:

1. Gravity (what if the house is on Moon - I/6th of gravity)
2. Outside Pressure - (Poles vs. Equator vs. Moon or Mars) or everything under water (Balloons as well as Home)
3. Buoyancy of the gas used (Hydrogen vs. Helium vs. Hot Air Balloon)
4. Weight of the House (Fiber vs. concrete vs. Wood)

The weight of the balloon and ropes can be considered negligible if we are considering a real house

Mathematically,
We need to calculate the net upward Force (Buoyancy) generated by balloon of volume V, by replacing equal amount of air (or water) around it.

F (net) = Upward force of balloon - Force of medium displaced

In order for home to get lifted

F(net) has to balance F (home)

F(net) is directly proportional to Volume of air replaced
F (net) ~ V (volume)

V = nv (n = number of balloons, v is volume of balloons)

n = V/v