Thought I just did this one.
Total of 90 fish:
c + p = 90
Charlie gave 1/4 c to Peter. Now
Charlie has c - (1/4) c
Peter has p + (1/4) c
Peter gave 2/5 of his to Charlie. Now
Peter has p + (1/4) c - 2/5( p + (1/4) c )
Charlie has c - (1/4) c + 2/5( p + (1/4) c )
And then they had equal number:
c - (1/4) c + 2/5( p + (1/4) c ) = p + (1/4) c - 2/5( p + (1/4) c )
Let's do the easy subtractions then multiply by 20 to clear the fractions,
(3/4) c + 2/5( p + (1/4) c ) = 3/5( p + (1/4) c )
15c + 8p + 2c = 12p + 3c
14c = 4p
7c = 2p
c + p = 90
2c + 2p = 180
2c + 7c = 180
9c = 180
c = 20
p = 70
Answer: Charlie started with 20, Peter with 70
Check:
Initially C:20, P:70
1/4(20)=5 to P
C:15, P:75
(2/5) 75 = 30 to C
C:45, P45
Good