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Section 20 of the New Series, Volume 1

Three thousand four hundred and ten taels of silver,
Distributed among five merchants according to their capital shares.
The original silver follows a "two-to-eight" succession,

The poem warns against using simplified or "shorthand" accounting tricks that might obscure the true proportions of the distribution.

The Answer says:

A: 2,560 taels
B: 640 taels
C: 160 taels
D: 40 taels
E: 10 taels
The names 甲 (Jiǎ), 乙 (Yǐ), 丙 (Bǐng), 丁 (Dīng), and 戊 (Wù) are the first five Heavenly Stems, used here as placeholders for five people, which we translate as A, B, C, D, and E.

The Explanation says:

The number 2 implies that for every tael, the next person receives 4 times as much. The "two-to-eight" ratio mentioned in the poem refers to a 2:8 ratio, which is 1:4. Thus, each successive partner’s share is four times larger than the previous one. Therefore, starting from E and moving upward, successively multiply by 4. This is the method of "Summing the Proportional Weights" 衰併: cuī bìng, the process of adding individual proportional factors to find a total divisor.

The Method says:

List the proportional weights 衰: cuī, weights or ratios assigned to each party as follows:
E is 2;
D is 8;
C is 32;
B is 128;
A is 512.
These weights represent a geometric progression: $2 \times 4 = 8$; $8 \times 4 = 32$; $32 \times 4 = 128$; $128 \times 4 = 512$.

Summing these together yields 682, which serves as the divisor 法: fǎ, the number used to divide the total amount.
Take the total silver to be divided, 3,410 taels, as the dividend 實: shí, the total quantity being partitioned.

Divide the dividend by the divisor to get 5, which represents the value of a single unit of weight. Multiply this unit value by each party's weight to obtain the individual amounts, which matches the problem 合問: hé wèn, a phrase indicating the calculation has been verified.
Example calculation: For person E, $2 \times 5 = 10$ taels. For person A, $512 \times 5 = 2,560$ taels.