Excess and Deficit
Certain items are purchased jointly. If each person pays 8 coins, the surplus is 3 coins, and if each person gives 7 coins, the deficiency is 4 coins. Find the number of people and the total cost of the items?
Calculate the average price each person would pay so there is no excess or deficit.
The answer is 7.571.
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This problem can be easily solved by Gaussian elimination. The answer is 53 coins divided evenly among 7 people. However, the book in which this question was taken uses Cramer's rule to solve, which involves determinants. What is interesting is that this method for solving 2 × 2 matrices existed in ancient China 2200 years ago.
Source: Jiu Zhang Suan Shu