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Math Help - Mixing problem

  1. #1
    Junior Member
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    Mixing problem

    A country has 5 billion in paper currency. Each day, 30 million is deposited into banks and the same amount loaned out. There is a regime change and each day the 30 million is replaced by a new currency when loaned out. How long will it take for 90% of the currency to be new?

    I know the answer, but I'm having trouble arriving at it.
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  2. #2
    Senior Member Sambit's Avatar
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    If the new currencies of one day are not changed with the new currencies of the following days, then you need to solve 30n=5000(90/100). The solution is n=150
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  3. #3
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    The solution is 384. Not all of the money coming in is old after day 1. Thanks though, I solved it last night.
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