Let's denote the mass of each lump of gold as x. According to the problem, we have four identical lumps of gold on one side, which we can represent as 4x. On the other side, we have one identical lump of gold with a mass of x and a 22 kg mass. Thus, the equation can be written as:
4x = x + 22 kg
By simplifying the equation, we get:
4x - x = 22 kg
3x = 22 kg
Finally, we can solve for x:
x = 22 kg / 3
Therefore, the mass of each lump of gold is approximately 7.33 kg.