# Math Help - Mixing problem

1. ## 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.

2. 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 $n=150$

3. The solution is 384. Not all of the money coming in is old after day 1. Thanks though, I solved it last night.