Chiu Chang Suann Jing/Examples/Example 5

Example of Problem from

 * 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?

Solution
The first class bundle contains $9 \frac 1 4$ measures.

The second class bundle contains $4 \frac 1 4$ measures.

The third class bundle contains $2 \frac 3 4$ measures.

Proof
Let $x$, $y$ and $z$ denote the measures of grain contained in one bundle of each of the $1$st, $2$nd and $3$rd class respectively.

We have: