Final answer:
To find the number of fish Mike had at first, work backwards from the given information. Mike originally had 50 fish in his collection.
Step-by-step explanation:
To find the number of fish Mike had at first, we need to work backwards from the given information.
Mike gives 2/3 of his fish to the high school. This means he has 1 - 2/3 = 1/3 of his original fish remaining.
He then gives 2/5 of the remaining fish to the elementary school. This means he has 1 - 2/5 = 3/5 of 1/3 of his original fish remaining.
We know that 3/5 of 1/3 of his original fish is equal to 30 fish. Let's set up an equation to solve for the original number of fish, 'x':
(3/5) * (1/3) * x = 30
Multiplying both sides by (5/3) to isolate 'x', we get:
x = 30 * (5/3) = 50
Therefore, Mike originally had 50 fish in his collection.