LEONARDO OF PISA, SON OF BONACCI, WAS CALLED FIBONACCI. HE IS PRIMA...

8. Leonardo of Pisa, son of Bonacci, was called Fibonacci. He is primarily knownto us through a problem on reproductive rabbits. However, that problem onlytook up half a page of his monumental work Liber Abaci, or The Book ofCalculations. What this book is to arithmetic is comparable to what Euclid -- TheElements is to geometry.The following problem is from Liber Abaci Chapter Thirteen, try to solve it.The first and second men said to the third and fourth, “If each of you gives us 1/3of your bezants, then we have just enough money to buy that horse.” The second and third men said to the fourth and fifth, “If each of you gives us 1/4of your bezants, then we have just enough money to buy the same horse.” The third and fourth men said to the fifth and first, “If each of you gives us 1/5 ofyour bezants, then we have just enough money to buy the same horse.” The fourth and fifth men said to the first and second, “If each of you gives us 1/6The fifth and first men said to the second and third, “If each of you gives us 1/7How many bezants did each man have and how many bezants did the horse cost?(All the five men had a positive integral number of bezants; the cost of horse isalso a positive integral number of bezants less than 5000.)The horse costs bezants, the first man has bezants,

Answer :

the second man has bezants, the third man has bezants,the fourth man has bezants, the fifth man has bezants.2009 AsiaInter-CitiesTeenagersMathematics Olympiad

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