There are 49 dogs signed up to compete in the dog show. There are 36 more small dogs than large dogs signed up to compete. How many small dogs are signed up to compete?

Hello. Let's assign s for the number of small dogs and l for the number of large dogs. Knowing that there are 36 more small dogs than large ones, we can have the following equation to represent the relation between these two:
[tex]s=l+36[/tex]

Since there are 49 dogs in the dog show, the sum of small dogs and large dogs should equal 49. We write this in equation form and solve for l.

[tex]s+l=49[/tex]
[tex](l+36)+l=49[/tex]
[tex]2l+36=49[/tex]
[tex]2l=13[/tex]
[tex]l=6.5[/tex]

Therefore, there are 6.5 large dogs in the dog show. (This number may not be realistic since we don't have half a dog but it works for brushing up our math skills.)

To find the number of small dogs, we simply add 36 to the number of large dogs.

[tex]s=l+36=6.5+36=42.5[/tex]

ANSWER: There are 42.5 small dogs in the dog show.