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Math Help - fraction problem

  1. #1
    Junior Member
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    Pennsylvania
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    fraction problem

    The king took a cup filled with juice and drank 1/5 of its contents. When the king looked away, the court jester refilled the cup by adding water to the remaining juice and then stirring. The king drank of this mixture. When the king looked away again, the jester refilled the cup with more water and stirred, and the king drank 1/3 of this mixture. When the king looked away a third time, the jester refilled the cup with more water. What percentage of this final mixture was water
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  2. #2
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    Nov 2008
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    once the king drinks 1/5 of the drink and the jester refils, the percentage of juice to water is 80% juice 20% water yes?

    then 1/4 is drunk, so take 1/4 off 20% and 80% to get 15%(3/4 of 20%) and 60%(3/4 of 80%), then the jester fills the water up to 40% (as this is what is required to make up 100% of the juice).

    Then 1/3 is drunk so again take this from 40% and 60% to get 26.667% water and 40% juice.

    Then finally water is added to make up 100% so if the juice has depleted to 40% then the mixture is made up of 60% or 3/5 water.

    hope this helps
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