Let the weights in kilograms of the head and body of the fish be h and b respectively. Then

h = 9 +

1 3

b

and b = h+9. So

b = 9 +

1 3

b + 9

, that is,

2 3

b = 18

, which gives b = 27. Hence h = 18, so the whole fish weighed 54kg.