An Animal shelter has 100 animals.

Question

An animal shelter has a total of 100100 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than one-half the number of cats, and there are 20 more cats than dogs, how many of each animal are at the shelter?

Answer 1

Hi Ali,

If an animal shelter has 100 animals comprised of cats, dogs, and rabbits there would be 50 cats, 30 dogs, 20 rabbits.

Explanation:

In this explanation I will be using c for cats, d for dogs, and r for rabbits.

100 animals comprised of cats, dogs, and rabbits: 100=c+d+r

rabbits is 5 less than one-half the number of cats: r=(0.5c)-5

20 more cats than dogs: c=d+20

Now we found our three equations for our three variables:

100=c+d+r

r=(.5c)-5

c=d+20, this one can be changed to d=c-20 so that we can substitute each variable with its equation, to find c like this: 100=c+(c-20)+(.5c-5) c = 50

now, you can plug c into the equation for d to find d, and into the equation for r to find r: d=50-20 d = 30 AND r=(.5*50)-5 r = 20

To double check your work you can plug each variable back into the original equation to make sure it equals 100: 50+30+20=100

:)

Answer 2

C + D + R = 100

1/2 the no. of cats is C/2; 5 less than the no. of cats = C/2 - 5 = R (Rabbits)

20 more cats than dogs: C = D + 20 (so D = C - 20)

Substitution in 1st eqn: C + (C - 20) + (C/2 - 5) = 100

5C/2 = 125 → 5C = 250 → C = 50 cats

Then D = 50 - 20 = 30 dogs

The balance of the 100 are rabbits (20) or R = 50/2 - 5 = 25 - 5 = 20