Answer: There are 180 dogs in the shelter.
Step-by-step explanation:
Let be "c" the number of cats in the shelter and "d" the number of dogs in the shelter.
You know that the total number of dogs and cats in the animal shelter is 275. Then you can express this with:
[tex]d+c=275[/tex]
If the number of cats is 5 more than one half of the number of dogs, you can express it with:
[tex]c=\frac{d}{2}+5[/tex]
Then, substitute [tex]c=\frac{d}{2}+5[/tex] into [tex]d+c=275[/tex] and solve for "d" to calculate the number of dogs that are in the shelter. Then:
[tex]d+c=275\\\\d+\frac{d}{2}+5=275\\\\d+\frac{d}{2}=275-5\\\\\frac{2d+d}{2}=270\\\\\frac{3d}{2}=270\\\\3d=270*2\\\\d=\frac{540}{3}\\\\d=180[/tex]
