Mike has a large tropical fish collection.He gives 2/3 of his fish to a local high school. Then gives 2/5 of the remaining fish to an elementary school. In the end, he has 30 fish left. How many...

Mike has a large tropical fish collection.He gives 2/3 of his fish to a local high school. Then gives 2/5 of the remaining fish to an elementary school. In the end, he has 30 fish left. How many fish did mike have at first.

Expert Answers
justaguide eNotes educator| Certified Educator

Mike has a large tropical fish collection.

Let the number of fish that Mike has be X.

He gives `2/3` of his fish to a local high school. The number of fish remaining with him is `(1 - 2/3)*X = X/3`

Then, he gives `2/5` of the remaining fish to an elementary school. The number remaining with him now is `(X/3)*(1 - 2/5)` = `(X/3)*(3/5) = X/5`

He has 30 fish left finally. `X/5 = 30`

=> X = 150

Mike had 150 fish to start with.

tonys538 | Student

Mike has a large tropical fish collection. He gives 2/3 of his fish to a local high school. Then gives 2/5 of the remaining fish to an elementary school. In the end, he has 30 fish left.

The number of fish left with Mike at the end is 1 - 2/5 = 3/5 of the number he had after he gave part of his fish to the high school. The number of fish he had after he had given some to the high school is 30/(3/5) = 150/3 = 50

As he gave 2/3 of his fish to the high school, 50 is the number equal to 1/3 of the original number of fish he had. This gives the number of fish he had at first as 50/(1/3) = 50*3 = 150

Mike had 150 fish at first.