《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III"
§23. Multiplication determining a total (4)

This section gives a word problem where multiplication is used to determine totals.

The relevant unit conversion for capacity is

1 \unit{barrel~(斛)} = 100 \unit{quarts~(升)}.

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
今有六萬口、上口三萬人、日食九升、中口二萬人、日食七升、下口一萬人、日食五升。	Suppose there be [a] population of six myriad: [an] upper population [being] three myriad people, [each] day eating nine quarts; [a] middle population, two myriad people, [each] day eating seven quarts; [and a] lower population, one myriad people, [each] day eating five quarts.	口： population; lit. mouths
問上中下口共食幾何。	[We] ask, how much altogether eat [the] upper, middle, [and] lower populations?
答曰、四千六百斛。	Answer saith: four thousand six hundred barrels.
術曰、各置口數、以日食之數乘之。	Method saith: put [down] each population's number, [and] multiply it by [the] number eaten [each] day.
所得、并之、即得。	[Of] those which result, combining them, [we] are done.	In modern notation, \begin{aligned} & 30000 \times \frac{9 \unit{quarts}}{\unit{day}} + 20000 \times \frac{7 \unit{quarts}}{\unit{day}} + 10000 \times \frac{5 \unit{quarts}}{\unit{day}} \\[\tallspace] &= \frac{460000 \unit{quarts}}{\unit{day}} \\[\tallspace] &= \frac{4600 \unit{barrels}}{\unit{day}}. \end{aligned}

Conway (2023). "Sun Tzŭ's Computational Classic: Volume III §23". <https://yawnoc.github.io/sun-tzu/iii/23> Accessed yyyy-mm-dd.