Let the number of large dogs = x.
Given 36 more small dogs than large dogs.
So number of small dogs =

Given total 49 dogs signed up for dog show.
So we can write the equation as small dogs + large dogs = total dogs.



We have to move 36 to the other side now by subtracting it from both sides.



To get x, we have to move 2 to the other side by dividing it to both sides.


So there are 6.5 large dogs are signed up.
Number of small dogs =

So there are 42.5 small dogs.
But there can not be a decimal number for number of dogs.