What was the amount of wine originally in Li Bai’s jug?
(Tang
Thursday, June 11, 2009
Solving Historical Elementary Mathematics Problems #3
Poet Li Bai’s jug contained some wine. Every time he passed by a wine shop, he would top up the wine in the jug so that the amount was doubled. When he passed by beautiful flowers, he would drink 1 litre of wine from the jug. Along the way, he passed by wine shops and beautiful flowers three times alternatively and finished all the wine in the jug.
What was the amount of wine originally in Li Bai’s jug?
(TangDynasty , China
What was the amount of wine originally in Li Bai’s jug?
(Tang
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By working backwards...
ReplyDeleteAt Beautiful Flowers (end) = 0 + 1 = 1 litre
At Wine Shop = 1 / 2 = 0.5 litre
At Beautiful Flowers = 0.5 + 1 = 1.5 litres
At Wine Shop = 1.5 / 2 = 0.75 litres
At Beautiful Flowers = 0.75 + 1 = 1.75 litres
At Wine Shop (Beginning) = 1.75 / 2 = 0.875 litres
Ans: 0.875 litres??
still thinking......
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ReplyDeleteIt must end at the flower shop,which means there is 1litre before he drinks it.This is the top up of the wine at the wine shop.So 1litre/2=500ml.When see beautiful flower he drinks 1litre,so 1litre+500ml=1litre500ml. This is the top up for the wine,so 1litre500ml/2=750ml.Now add:1litre +750ml=1750ml(when he sees beautiful flower).This is the answer,1750ml/2=875ml!
ReplyDeleteAnyway what does it means by 3 times alternatively.We don't understand:(
ReplyDeleteIf not,is the answer 1 litre 500ml?
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ReplyDeleteI think that the answer has to be solved using backwards, like Han Chen:
ReplyDeleteHe must end at the flower shop as if he ends at the wine shop, his wine would increase.
So, at the flower shop, he would increase his wine by 1 litre.
Next, he went to the wine shop and decrease his wine by dividing two. the answer would be 500ml.
He went to the flower shop and increase his wine to be 1500ml.
He again went to the wine shop and his wine became 750ml.
He went to the flower shop and his wine became 1750ml.
Finally, he went to the wine shop and his wine became 875ml.
The answer is then 875ml.
My answer is definitely correct!!
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