Answer:
[tex]S=42\frac{1}{2}[/tex] small dogs
Step-by-step explanation:
Let [tex]L[/tex] be the number of large dogs and [tex]S[/tex] be the number of small dogs.
Since it is given that the toal number of dogs that signed up is 49, this makes our first equation [tex]L+S=49[/tex].
Also, there are 36 more small dogs than large dogs that signed up to compete, so this makes our second equation [tex]S=L+36[/tex].
Since the value of [tex]S[/tex] is already solved in our second equation, we can plug it into the first equation and solve for [tex]L[/tex]:
[tex]L+S=49[/tex]
[tex]L+(L+36)=49[/tex]
[tex]L+L+36=49[/tex]
[tex]2L+36=49[/tex]
[tex]2L=13[/tex]
[tex]L=\frac{13}{2}[/tex]
[tex]L=6\frac{1}{2}[/tex]
Now plug the value of [tex]L[/tex] into either equation and solve for [tex]S[/tex]:
[tex]S=L+36[/tex]
[tex]S=\frac{13}{2}+36[/tex]
[tex]S=\frac{85}{2}[/tex]
[tex]S=42\frac{1}{2}[/tex]
Even though the answer isn't realistic, it's still correct.
