Math & Physics Problems Wikia
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Problem

今有共買物,人出八,盈三;人出七,不足四。問:人數、物價各幾何?

Suppose there is an item bought in common. If each person pays 8 coins, there is an excess of 3 coins; if each person pays 7 coins, there is a deficiency of 4 coins. Question: What is the number of people, and what is the price of the item?

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Solution

Let be the number of people, and the price of the items in coins.

Write the problem as a system of linear equations:

Use Cramer's rule

There are 7 people, and the items cost 53 coins.

Note: The method employed in the Jiuzhang Suanshu is actually the method of Double False-Position, which turns out to be equivalent to Cramer's rule for 2 x 2 systems of linear equations.

Excess:

Deficit:

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