Question

help for30 stars for right answer At the animal shelter that houses cats and dogs, 9/23 of all animals are cats. If one fourth of each type of animal is boy, and there are 27girl cats, what is the number of girl dogs in the shelter ?

Answer 1

Answer:

The number of girl dogs are $42$

Step-by-step explanation:

The animal shelter only houses cats and dogs.

The proportion of cats = $\frac{9}{23}$

Therefore, the proportion of dogs = $\frac{14}{23}$

And $\frac{1}{4}$ of each animal type is a boy.

If there are 27 girl cats, that means 27 represents $\frac{3}{4}$ of the cat population.

So we can now find the number of boy cats in the shelter,

$\frac{27}{\frac{3}{4} }*\frac{1}{4}$

=$\frac{27*4}{3*4}$

=$\frac{27}{3}$

=$9$

So the total number of boy cats are 9.

Total number of cats = Number of girl cats + Number of Boy cats

                                   = $27+9$

                                   =$36$

36 cats represents $\frac{9}{23}$ proportion of the total animals.

Therefore, we can find the total number of dogs in the shelter,

$\frac{36}{\frac{9}{23} }*\frac{14}{23}$

=$\frac{36*23*14}{9*23}$

=$\frac{36*14}{9}$

=$\frac{4*14}{1}$

=$56$

So the total number of dogs are 56.

Out of this 56 $\frac{3}{4}$ of the dogs are girls.

Therefore,

The number of girl dogs = $56*\frac{3}{4}$

=$42$