《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III"
§6. Division utilising a rate (1)

This section gives a word problem where division by a rate is used to determine an amount.

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
今有租九萬八千七百六十二斛、欲以一車載五十斛。問用車幾何。 Suppose there be land-tax nine myriad eight thousand seven hundred [and] sixty-two barrels, [and we] wish to use one chariot [to] carry fifty barrels. [We] ask, how many chariots useth [it]?
答曰、一千九百七十五乘奇一十二斛。 Answer saith: one thousand nine hundred [and] seventy-five chariots remainder twelve barrels.
術曰、置租九萬八千七百六十二斛為實、以一車所載五十斛為法。 Method saith: put [down the] land-tax nine myriad eight thousand seven hundred [and] sixty-two barrels as [the] dividend, [and] use that carried of one chariot, [even] fifty barrels, as [the] divisor.
實如法、即得。 [Taking the] dividend as [per the] divisor, [we] are done.
  • In modern notation,
    \frac{98762 \unit{barrels}}{50 \unit{barrels} / {\unit{chariot}}} = 1975 \unit{chariots} + \frac{12 \unit{barrels}}{50 \unit{barrels} / {\unit{chariot}}}.

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume III §6". <https://yawnoc.github.io/sun-tzu/iii/6> Accessed yyyy-mm-dd.