Systematic Treatise on Arithmetic, Volume 14

The method says: List the eight proportional shares ①②③④⑤⑥⑦⑧. Multiply each by the difference of three years to determine each person's share-number The "share" (衰, shuai) is a proportional weighting factor used in pre-modern Chinese mathematics to solve distribution problems.
The eldest son's share results in 12; the second son's share results in 16; the third son's share results in 19; the fourth son's share results in 25;
the fifth son's share results in 31; the sixth son's share results in 38; the seventh son's share results in 42; the eighth son's share results in 48.
Summing these shares gives 180. Subtract this from the total of 720 The total of 720 and the specific shares listed here appear to be a variation or a calculation error relative to the problem on the previous page, which stated a total age of 207. The remainder is 90. Divide this by the number of people nine sons to get 10 years, which is the age of the ninth son. Successively add three years to each son until reaching the eldest to match the requirements of the question.

Song of Money According to Rank

Jia, Yi, Bing, Ding, Wu, Ji, and Geng— These are the first seven "Celestial Stems," used here as placeholders for seven people, much like "A, B, C, D..."
The capital of these seven people is not equal.
Jia and Yi have twenty-three point seven in paper currency 23 taels, 7 mace;
twenty-six point one for Wu, Ji, and Geng 26 taels, 1 mace.
Only Bing and Ding have no amount recorded;
They must be divided clearly according to their rank.
May I ask the master who is capable of such proportions,
To deduce and calculate this in detail without error or dispute.

Systematic Treatise on Arithmetic original: 算法統宗 (Suànfǎ Tǒngzōng), a famous 16th-century mathematics manual by Cheng Dawei; Proportional Share original: 衰 (shuāi), a method of proportional distribution; Paper Currency original: 鈔 (chāo), referring to Ming Dynasty paper money; Celestial Stems original: 甲乙丙丁戊己庚 (Jiǎ-Yǐ-Bǐng-Dīng-Wù-Jǐ-Gēng); Twenty original: 念 (niàn), a traditional shorthand for 廿 or twenty