This is a math question

Question

An animal shelter has a total of  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 Anna

Let c, d and r represents cats,dogs and rabbits simultaneously.

According to ques

c + d + r = 150 .............(i)

Number of rabbits :

r = 1/2c - 5

c = 2(r + 5) .............(ii)

Number of cats

c = d + 20

d = c - 20

d = 2(r + 5) - 20 .............(iii) (replaced value of c from eq (ii))

Now, putting the values of eq (ii) and (iii) in eq (i)

2(r + 5) + 2(r + 5) - 20 + r = 150

2r + 10 + 2r + 10 - 20 + r = 150

5r = 150

r = 30

c = 2(r + 5)

c = 2(30 + 5)

c = 70

d = c - 20

d = 70 - 20

d = 50

therefore, there were 70 cats, 50 dogs and 30 rabbits

Answer 2

Hi Anna!

so what I would do is first label the variables:

c=cats

d= dogs

r=rabits

Then I would write an equation that equals the total sum of animals using the variables:

c+d+r= 150

then reading the question, I would come up with mini equations that I can substitute into the eq. above:

r=1/2c-5 or c= 2r+10

c= 20+d or d= c-20--> d= (2r+10) - 20 (then simply into d=2r-10)

Then I would try to solve for 1 variable by shift in the top equations around a bit such as did with the second options and then put them into the original equation by solving for r

(2r+10) +(2r-10) + r= 150

in the equation right above, the value of 10 would cancel out and you would be left with: 5r= 150 (add up all the r values)

r= 30

Lastly go back to the equations for the dogs and cats and substitute the r for 30:

c= 2(30)+10= 70

d=2(30)-10= 50

Now check to see if they all add up to 150:

70+50+30= 150

and finally check if those values work for the conditions asked

such as:

rabbits have to 1/2 of the value of cats-5

which is 1/2(70)-5= 30

and that there are 20 more cats than dogs which is true because 70-50 is 20

Therefore the answer is= 30 rabbits, 50 dogs and 70 cats