Respuesta :
Answer:
There are 126 dogs, 86 cats and 42 guinea pigs at shelter.
Step-by-step 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:
[tex]C+D+G=254...(1)[/tex]
Further, the number of guinea pigs is one third the number of dogs. We can represent this information in an equation as:
[tex]G=\frac{1}{3}*D...(2)[/tex]
There are 40 more dogs than cats. We can represent this information in an equation as:
[tex]D=C+40...(3)[/tex]
Upon substituting equation (2) and (3) in equation (1), we will get:
[tex](D-40)+D+\frac{1}{3}*D=254[/tex]
[tex]D-40+D+\frac{D}{3}=254[/tex]
[tex]D-40+40+D+\frac{D}{3}=254+40[/tex]
[tex]2D+\frac{D}{3}=294[/tex]
Make a common denominator:
[tex]\frac{6D}{3}+\frac{D}{3}=294[/tex]
[tex]\frac{6D+D}{3}=294[/tex]
[tex]\frac{7D}{3}=294[/tex]
[tex]\frac{7D}{3}*3=294*3[/tex]
[tex]7D=882[/tex]
[tex]\frac{7D}{7}=\frac{882}{7}[/tex]
[tex]D=126[/tex]
Therefore, there are 126 dogs at the shelter.
Substitute [tex]D=126[/tex] in equation (2):
[tex]G=\frac{1}{3}*126[/tex]
[tex]G=42[/tex]
Therefore, there are 42 guinea pigs at the shelter.
Substitute [tex]D=126[/tex] in equation (3):
[tex]126=C+40[/tex]
[tex]126-40=C+40-40[/tex]
[tex]86=C[/tex]
Therefore, there are 86 cats at the shelter.
