Nicholas has a larger tropical fish collection. he gives 2/3 of his fish to a high school. then he gives 2/5 of the remaining fish to another school. in the end he has 30 fish left. how many fish nicolas have at first?

Let the initial count of his fish be n.

He gives away 2/3 of these fish:  2n/3, leaving n/3 fish.

He gives away 2/5 of these remaining n/3 fish:  (2/5) times (n/3), or 

2n
--- , meaning that (3/5) times (n/3) fish are left.
15

(3/5)(n/3) = n/5 fish left = 30 fish.  Thus, n = 150 fish.

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