[867V309]

One should never enter 1/2 of a dog into a dog show.

well, if it shows well, it's probably a winner.

but seriously, X + (X+36)=49 or large dogs+(large dogs+36)=49     that's wrong

it should be (X+36)=49 or (Xlarge dogs+36small dogs)=49

So X= large dogs = 49-36=13.   

How many small dogs are signed up to compete?:

49(all dogs)-13(large dogs)=36(small dogs.)

[867V309]

sorry, misread the problem...