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Systematic Treatise on Mathematics, Volume 14

Verse

Three hundred and sixty-nine catties of silk floss,

Four guests wish to divide it among themselves.

The original shares are all calculated at an eighty-percent rate,

Ensure not a single guest receives even a tiny bit less.

The "eighty-percent rate" (八折, bā zhé) indicates a geometric progression where each subsequent person receives 0.8 times the amount of the person preceding them.

The Answer says:
A: 125 catties
B: 100 catties
C: 80 catties
D: 64 catties
The text uses the Heavenly Stems 甲 (Jiǎ), 乙 (Yǐ), 丙 (Bǐng), and 丁 (Dīng) as placeholders for the four people, which are translated here as A, B, C, and D.

The Method says:
List the proportional weights 衰: cuī, ratios or weights assigned to each share as follows:
A 1,000; B 800; C 640; D 512.
These weights are derived by starting with 1,000 and repeatedly multiplying by 0.8 (e.g., 1000 × 0.8 = 800; 800 × 0.8 = 640, etc.).
Sum these to get 2,952, which serves as the divisor 法: fǎ, the number used to divide the total</term.
Separately, take the 369 catties of silk floss to be divided and multiply it by each of the individual proportional weights before they were summed.

For A, the product is 369,000.
For B, the product is 295,200.
For C, the product is 236,160.
For D, the product is 188,928.
In traditional Chinese mathematics, these products are called the "dividends" (實, shí).

Divide these dividends by the divisor 2,952 to obtain the correct amount of silk floss for each person as requested.
For example, 369,000 ÷ 2,952 = 125.