In the farm pet club pet show, 44 pets are entered. There are 3 times as many dogs as cats and half as many ferrets as dogs. How many of each are there?
let the number of cats be c
then the number of dogs is 3c
and the number of ferrets is 3c/2
c + 3c + 3c/2 = 44
multiply be 2
2c + 6c + 3c = 88
I am sure you can finish it from there
To determine the number of cats, dogs, and ferrets in the farm pet club pet show, we can break down the problem step by step.
Let's assign variables to the number of cats, dogs, and ferrets. Let's call the number of cats "C," the number of dogs "D," and the number of ferrets "F."
According to the problem, we know the following information:
1. There are 44 pets entered in total: C + D + F = 44.
Next, we can use the given information to form additional equations:
2. There are 3 times as many dogs as cats: D = 3C.
3. There are half as many ferrets as dogs: F = 0.5D.
Now, we can use substitution to solve the system of equations:
Substitute equation 2 into equation 3:
F = 0.5(3C)
F = 1.5C
Substitute equations 2 and 3 into equation 1:
C + 3C + 1.5C = 44
Combine like terms:
5.5C = 44
Divide both sides by 5.5:
C = 44 / 5.5
Simplify:
C = 8
Now that we know the value of C, we can find D and F:
D = 3C
D = 3(8)
D = 24
F = 1.5C
F = 1.5(8)
F = 12
Therefore, there are 8 cats, 24 dogs, and 12 ferrets in the farm pet club pet show.