Distributing Original Silver by the "Four-Six" Successive Ratio

The Answer says:

A 4,406 taels, 4 mace
B 2,937 taels, 6 mace
C 1,958 taels, 4 mace
D 1,305 taels, 6 mace
The names 甲 (Jiǎ), 乙 (Yǐ), 丙 (Bǐng), and 丁 (Dīng) are the first four Heavenly Stems, used here as placeholders for four people or entities, similar to A, B, C, and D.

The Explanation says:

The "Four-Six" ratio This refers to a ratio of 4 to 6, or 2:3. In this calculation, it means each successive person receives 1.5 times the amount of the person below them. means that for every tael, there is an additional 5 0.5. Therefore, starting from D and moving upward, successively add 5 to determine the proportional weights 衰: cui, proportional factors or weights assigned to different parties. Sum these to create the divisor, then divide the dividend.

The Method says:

Arrange the proportional weights for each party: ① 8, ② 12, ③ 18, ④ 27. These weights follow a geometric progression: $8 \times 1.5 = 12$; $12 \times 1.5 = 18$; $18 \times 1.5 = 27$. Summing these yields 65, which serves as the divisor 法: fa, the number used to divide the dividend. Separately, take the total silver of 10,608 taels and multiply it by each party's weight:

〇 For A, the weight of 27 yields 286,416
〇 For B, the weight of 18 yields 190,944
〇 For C, the weight of 12 yields 127,296
〇 For D, the weight of 8 yields 84,864

Each of these results serves as a dividend 實: shi, the number to be divided. Divide each by the divisor 65, and the results will match the question.

Rhyme