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Silver and Gold

There are two piles; one containing 9 gold coins, the other 11 silver coins.  The two piles have the same weight.  One coin is taken from each pile and put in the other.  It is now found that the pile of mainly gold weighs 13 liang less than the pile of mainly silver coins.  Find the weight of a silver and a gold coin.

Jiuzhang Suanshu (The Nine Chapters on the Mathematical Art), c. 100 BCE

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"Silver and Gold," Convergence (March 2007)