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

The number of girl dogs are
`42`

Explanation:

The animal shelter only houses cats and dogs.

The proportion of cats =
`(9)/(23)`

Therefore, the proportion of dogs =
`(14)/(23)`

And
`(1)/(4)` of each animal type is a boy.

If there are 27 girl cats, that means 27 represents
`(3)/(4)` of the cat population.

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

`(27)/((3)/(4) )*(1)/(4)`

=
`(27*4)/(3*4)`

=
`(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
`(9)/(23)` proportion of the total animals.

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

`(36)/((9)/(23) )*(14)/(23)`

=
`(36*23*14)/(9*23)`

=
`(36*14)/(9)`

=
`(4*14)/(1)`

=
`56`

So the total number of dogs are 56.

Out of this 56
`(3)/(4)` of the dogs are girls.

Therefore,

The number of girl dogs =
`56*(3)/(4)`

=
`42`