Ancient Egyptian 'algebra': The method of 'false position' (estimate, check, adjust)

During the reign of HongWu, the first emperor of the Ming Dynasty of China, corruption of government officials was rampant and the emperor was very determined to wipe it out. Officials who embezzled more than the equivalent of 60 liang (one liang was around 30 grams) of silver were to be beheaded and then flayed, the skin publicly exhibited. The problem we have is inspired by this.

During a severe drought, relief funds were passed down from the central government to the provincial/municipal governments to aid affected people in the region. It has been a 'tradition' for these officials to embezzle a portion of these relief funds. When the funds were at the provincial government, the officials took half of it and passed on to the municipal government. Then the municipal government took half of the remaining funds before the funds were passed onto the people in need. In the end, the central government found out that a total of 90000 liang was missing. How much was the original amount of relief funds issued by the central government?

False Position:

We let x be the original amount of relief funds.

x/2 + x/4 = 90000

We try x = 60000 

60000/2 + 60000/4 = 45000

So we know 45000 is half of 90000, so we can just multiply the x by 2: 60000 * 2 = 120000.

120000/2 + 120000/4 = 90000

So a total of 120000 liang was issued by the central government.

Modern method: 

x/2 + x/4 = 90000

2x/4 + x/4  = 90000

3x/4 = 90000

x = 120000