Hot air balloon – Archimedes Principle

1. The problem statement, all variables and given/known data

A hot air balloon with V = 500 m^3 is floating in the air without moving. The air outside the balloon has a density of 1,20 kg/m^3, and the hot air inside the balloon has a density of 0,75 kg/m^3. Calculate the total mass of the hot air balloon.

2. Relevant equations

Archimedes Principle F0 = ρVg

3. The attempt at a solution

I googled the answer to this question, so I already know how to solve it:
F0 = (1,20 -0,75) * 500 = 225 kg

What I don´t understand is why g wasn´t integrated into this answer? How come the answer isn´t (1,20-0,75)*500 * 9,82 =2210 kg?

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