# Chiu Chang Suann Jing/Examples

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## Examples of Problems from

## 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?*