Chiu Chang Suann Jing/Examples

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?