Answer:
The number of girl dogs are [tex]42[/tex]
Step-by-step explanation:
The animal shelter only houses cats and dogs.
The proportion of cats = [tex]\frac{9}{23}[/tex]
Therefore, the proportion of dogs = [tex]\frac{14}{23}[/tex]
And [tex]\frac{1}{4}[/tex] of each animal type is a boy.
If there are 27 girl cats, that means 27 represents [tex]\frac{3}{4}[/tex] of the cat population.
So we can now find the number of boy cats in the shelter,
[tex]\frac{27}{\frac{3}{4} }*\frac{1}{4}[/tex]
=[tex]\frac{27*4}{3*4}[/tex]
=[tex]\frac{27}{3}[/tex]
=[tex]9[/tex]
So the total number of boy cats are 9.
Total number of cats = Number of girl cats + Number of Boy cats
= [tex]27+9[/tex]
=[tex]36[/tex]
36 cats represents [tex]\frac{9}{23}[/tex] proportion of the total animals.
Therefore, we can find the total number of dogs in the shelter,
[tex]\frac{36}{\frac{9}{23} }*\frac{14}{23}[/tex]
=[tex]\frac{36*23*14}{9*23}[/tex]
=[tex]\frac{36*14}{9}[/tex]
=[tex]\frac{4*14}{1}[/tex]
=[tex]56[/tex]
So the total number of dogs are 56.
Out of this 56 [tex]\frac{3}{4}[/tex] of the dogs are girls.
Therefore,
The number of girl dogs = [tex]56*\frac{3}{4}[/tex]
=[tex]42[/tex]
