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

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Mike has a large tropical fish collection. He gives 2/3 of his fish to the high school. Then he gives 2/5 of the remaining fish to the elementary school. In the end, he has 30 fish      Log On


   



Question 934484: Mike has a large tropical fish collection. He gives 2/3 of his fish to the high school. Then he gives 2/5 of the remaining fish to the elementary school. In the end, he has 30 fish left. how many fish did he have at first?
3/5 = 30; 3 units = 30
1 unit = 10
5 units = 50
50*3 = 150 fishes originally
Please show me how to do this problem algebraicaly.

Found 2 solutions by Fombitz, josmiceli:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
OK, originally he had X.
He gave the high school %282%2F3%29X which leaves him with %281%2F3%29X
He gave %282%2F5%29%281%2F3%29X to the elementary school which leaves him with %283%2F5%29%281%2F3%29X.
%283%2F5%29%281%2F3%29X=30
X=150

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the number of fish he started with
He gives +%28+2%2F3+%29%2Ax+ of his fish to the high school.
That means he has +%28+1%2F3+%29%2Ax+ left
--------------
he gives +2%2F5+ of the remaining fish to the elementary school.
+%28+2%2F5+%29%2A%28+1%2F3+%29%2Ax+ goes to the elementary school
--------------
He has +30+ fish left
This is telling you that:
+%28+1%2F3%29%2Ax+-+%282%2F5%29%2A%281%2F3%29%2Ax+=+%283%2F5%29%2A%281%2F3%29%2Ax+
is the number of fish he has left and
+%283%2F5%29%2A%281%2F3%29%2Ax+=+30+
+%283%2F15%29%2Ax+=+30+
+%281%2F5%29%2Ax+=+30+
+x+=+150+
He started with 150 fish
----------------------
check:
+%282%2F3%29%2A150+=+100+ goes to the high school
He has +50+ left
+%282%2F5%29%2A50+=+20+ goes to the elementary school
He has +30+ left
OK