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23.cmd
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< /resources/rules/yawnoc.cmdr
< /resources/rules/rendering.cmdr
< /resources/rules/equations.cmdr
< /resources/rules/language.cmdr
< /resources/rules/translation.cmdr
< /resources/rules/romanisation.cmdr
< /resources/rules/sun-tzu.cmdr
< /resources/rules/surrounds.cmdr
OrdinaryDictionaryReplacement: #.footer-properties-override
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* %copyright-prior-years --> get_year@%date-created--
OrdinaryDictionaryReplacement: #.boilerplate-properties-override
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* %cite-title --> '"Sun~Tz(uu)'s Computational Classic: Volume~III \S23"'
* %title --> "Sun~Tz(uu)'s Computational Classic: Volume~III" 《孫子算經卷下》 \S23
* %date-created --> 2022-11-20
* %date-modified --> 2023-03-04
- concluding_replacements:
#.yawnoc.typography
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* %%surrounds-up --> [^ Volume~III](./)
* %%surrounds-previous --> [<-- \S22](22)
* %%surrounds-current --> \S23
* %%surrounds-next --> [\S24 -->](24)
- concluding_replacements: #.surrounds.navigation-arrows
%%%
^^^^
- !home
- !top
- !sun-tzu
-{.breadcrumbed} !iii
-{.breadcrumbed} !!23
- !cite
^^^^
# .《孫子算經卷下》 "(Sun~Tz(uu)|孫子)'s Computational Classic: Volume~III" <br>
\S23. Multiplication determining a total~(4)
%%noscript-equations
%%surrounds
--
This section gives a word problem
where multiplication is used to determine totals.
--
--
The relevant unit conversion for capacity is
--
$$
1 \unit{barrel~(斛)} = 100 \unit{quarts~(升)}.
$$
--
See [Vol.~I \S3 (Units of capacity)](/sun-tzu/i/3).
--
##{#translation} Translation
--
Chinese source text: \a[72], \b[162], \c[52283], \d[84]. <br>
%%version-d-default
--
@@@@
<<
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,
$$
\begin{aligned}
&
30000 \times \frac{9 \unit{quarts}}{\unit{day}}
+ 20000 \times \frac{7 \unit{quarts}}{\unit{day}}
+ 10000 \times \frac{5 \unit{quarts}}{\unit{day}}
\\[\tallspace]
&=
\frac{460000 \unit{quarts}}{\unit{day}}
\\[\tallspace]
&=
\frac{4600 \unit{barrels}}{\unit{day}}.
\end{aligned}
$$
==
@@@@
%%surrounds
%%cite
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