[Axenolith]

There are only 2 sets, large and small dogs. 49 is the total and there are 36 more small than large, with only 2 sets. 36 is one of the sets.
X+36=49
Take 36 from each side
X=13
There are 13 large dogs.
That’s the answer.

The other way implies
# of large dogs + (# of large dogs + # of small dogs) = total # of dogs
Additionally, since only addition is taking place, the parenthetical is irrelevant. If they say the answer is fractional dogs, it’s freakin wrong.

[Axenolith]

The creator of that problem is probably the financial consultant for their health care program.

[publius911]

Looks like nobody can come up with the expected answer, without accepting a fractional dog to play a role.
So the solution must be an error in formulating the question.

[LukeL]

That is what the problem was suppose to say, but the problem said 36 MORE small dogs than large dogs. Your way there are only 23 more small dogs than large dogs.