Bexley gives Hershel 2/5*10 = <<2/5*10=4>>4 betta fish.
The total number of betta fish in the bowl is now 4+10 = <<4+10=14>>14
He also gives Hershel 1/3*15 = <<1/3*15=5>>5 goldfish
The total number of goldfish in the bowl is now 15+5 = <<15+5=20>>20
Counting the betta fish and goldfish, Hershel now has a total of 14 + 20 = <<14+20=34>>34 fish
When he gives his sister half of the fish, the remaining half is 34/2 = <<34/2=17>>17 fish
#### 17