•  From an ancient Chinese book (Chiu-chang Suan-shu - 200 B.C.).
3 sheaves of a good crop, 2 sheaves of mediocre crop, and 1 sheaf of bad crop are sold for 39 dou.
2 sheaves of good, 3 mediocre, and 1 bad are sold for 34 dou.
1 good, 2 mediocre and 3 bad are sold for 26 dou.
What is the price received for each sheaf of a good crop, each sheaf of a mediocre crop, and each sheaf of a bad crop?

Today this problem can be formulated as 3 equations in 3 unknowns, where x, y, and z represent the price of a good, mediocre, and bad crop, respectively:

•  I have Lemon Rum with an alcohol content of 30% and Rum with an alcohol content of 40%.  I want to get 300 ml of cocktail with an alcoholic strength of 25% by adding equal quantities of Lemon Rum and Rum to orange juice.  How much should I take from each of the three ingredients?

Let x, y, and z be the quantities (in ml) of Lemon Rum, Rum and orange juice.
x+y+z = 300 (300 ml of cocktail);  x−y = 0 (equal quantities of Lemon Rum and Rum);  30%·x + 40%·y = 25%·300 (Lemon Rum with 30% of alcohl, Rum with 40% of alcohl → 300 ml with 25% of alcohl).

107 ml of Lemon Rum and Rum, 86 ml of orange juice.

•  I have three bars made up of silver, copper and tin. Their compositions are:

```   silver copper  tin
1^  80%   17.5%   2.5%
2^  70%    25%     5%
3^  60%    30%    10%```

How much metal does it take from each bar to get a metal composed in the following way?
silver: 74%,  copper: 21.625%,  tin: 4.375%

Let x, y and z be the fractions that must be taken from each bar.