Chiu Chang Suann Jing/Examples
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Examples of Problems from Chiu Chang Suann Jing
Example $1$
- Two and a half piculs of rice are bought for $\frac 3 7$ of a tael of silver.
- How many piculs of rice can be bought for $9$ taels?
Example $2$
- Suppose that there are a number of rabbits and pheasants confined in a cage,
- in all thirty-five heads and ninety-four feet;
- required the number of each?
Example $3$
- A number of men bought a number of articles, neither of which are known;
- it is only known that if each man paid $8$ cash, there would be a surplus of $3$ cash,
- and if each man paid $7$ cash, there would be a deficiency of $4$ cash.
- Required the respective numbers?
Example $4$
- If $5$ oxen and $2$ sheep together cost $10$ taels of gold,
- and $2$ oxen and $5$ sheep together cost $8$ taels,
- what are the prices of oxen and sheep respectively?
Example $5$
- There are $3$ classes of corn, of which
- $3$ bundles of the first class,
- $2$ of the second class, and
- $1$ of the third class
- make $39$ measures.
- $2$ of the first,
- $3$ of the second, and
- $1$ of the third
- make $34$ measures.
- And:
- $1$ of the first,
- $2$ of the second, and
- $3$ of the third
- make $26$ measures.
- How many measures of grain are contained in $1$ bundle of each class?
Example $6$
- There is a pool $10$ feet square, with a reed growing vertically in the centre,
- its roots at the bottom of the pool, which rises $1$ foot above the surface;
- when drawn towards the shore it reaches exactly to the brink of the pool;
- what is the depth of the water?
Example $7$
- A chain suspended from an upright post has a length of $2$ feet lying on the ground,
- and on being drawn out to its full length, so as just to touch the ground,
- the end is found to be $8$ feet from the post.
- What is the length of the chain?
Example $8$
- There is a bamboo $10$ feet high,
- the upper end of which being broken down on reaching the ground,
- the tip is just $3$ feet from the stem;
- what is the height of the break?
Example $9$
- What is the largest circle that can be inscribed within a right-angled triangle,
- the two short sides of which are respectively $8$ and $15$?
Example $10$
- Of $2$ water weeds, one grows $3$ feet and one grows $1$ foot on the first day.
- The growth of the first becomes every day half of that of the preceding day
- while the other grows twice as much as the previous day.
- In how many days will the two grow to equal heights?