Question

An animal shelter has a total of 254 animals comprised of cats, dogs, and guinea pigs. If the number of guinea pigs is one third the number of dogs, and there are 40 more dogs than cats, how many of each animal are at the shelter?

Answer 1

There are 126 dogs, 86 cats and 42 guinea pigs at shelter.

Explanation:

Let C, D and G represent number of cats, dogs and guinea pigs respectively.

We have been given that an animal shelter has a total of 254 animals comprised of cats, dogs, and guinea pigs. We can represent this information in an equation as:

`C+D+G=254...(1)`

Further, the number of guinea pigs is one third the number of dogs. We can represent this information in an equation as:

`G=(1)/(3)*D...(2)`

There are 40 more dogs than cats. We can represent this information in an equation as:

`D=C+40...(3)`

Upon substituting equation (2) and (3) in equation (1), we will get:

`(D-40)+D+(1)/(3)*D=254`

`D-40+D+(D)/(3)=254`

`D-40+40+D+(D)/(3)=254+40`

`2D+(D)/(3)=294`

Make a common denominator:

`(6D)/(3)+(D)/(3)=294`

`(6D+D)/(3)=294`

`(7D)/(3)=294`

`(7D)/(3)*3=294*3`

`7D=882`

`(7D)/(7)=(882)/(7)`

`D=126`

Therefore, there are 126 dogs at the shelter.

Substitute
`D=126` in equation (2):

`G=(1)/(3)*126`

`G=42`

Therefore, there are 42 guinea pigs at the shelter.

Substitute
`D=126` in equation (3):

`126=C+40`

`126-40=C+40-40`

`86=C`

Therefore, there are 86 cats at the shelter.