Question

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?

Answer 1

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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