《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III"
§10. Division determining a rate (3)

This section gives a word problem where division is used to determine a rate. Specifically, it is the previous problem (§9) in reverse.

The relevant unit conversion for weight is

1 \unit{catty~(斤)} = 16 \unit{taels~(兩)}.

Translation

Chinese source text: Version A, Version B, Version C, Version D.
Unless noted otherwise, I follow the text from Version D, 《知不足齋叢書》本.

Source text	Target text	Notes
今有綿九萬一千一百三十五斤、給與三萬六千四百五十四戶。問戶得幾何。	Suppose there be silk-floss nine myriad one thousand one hundred [and] thirty-five catties, provided to three myriad six thousand four hundred [and] fifty-four households. [We] ask, how much getteth [each] household?
答曰、二斤八兩。	Answer saith: two catties [and] eight taels.
術曰、置九萬一千一百三十五斤為實、以三萬六千四百五十四戶為法。	Method saith: put [down the] nine myriad one thousand one hundred [and] thirty-five catties as [the] dividend, [and] use [the] three myriad six thousand four hundred [and] fifty-four households as [the] divisor.
除之、得二斤、不盡一萬八千二百二十七斤。	Dividing them, resulteth in two catties, remainder one myriad eight thousand two hundred [and] twenty-seven catties.
以一十六乘之、得二十九萬一千六百三十二兩。	Multiplying it by sixteen, resulteth in twenty-nine myriad one thousand six hundred [and] thirty-two taels.
以戶除之、即得。	Dividing it by [the] households, [we] are done.	In modern notation, \begin{aligned} \frac{91135 \unit{catties}}{36454 \unit{households}} &= \frac{2 \unit{catties}}{\unit{household}} + \frac{18227 \unit{catties}}{36454 \unit{households}} \times \frac{16 \unit{taels}}{\unit{catty}} \\[\tallspace] &= \frac{2 \unit{catties} + 8 \unit{taels}}{\unit{household}}. \end{aligned}

Conway (2023). "Sun Tzŭ's Computational Classic: Volume III §10". <https://yawnoc.github.io/sun-tzu/iii/10> Accessed yyyy-mm-dd.