In a pet shop one half of the animals are dogs.one fourth of the animals are bunnies. Six of the animals are cats. There are an equal number of cats and bunnies. How many dogs are there in the pet shop
Let A=number of animals, D=number of dogs, B=number of bunnies, and C=number of cats.
Given:
1/2*A = D
1/4*A = B
C = 6
C = B
Solution:
C=B=6
1/4*A=B=6
1/4*A=6
A=6*4=24
D=1/2*A
D=1/2*24
D=12
Therefore, there are 12 dogs.
Let's solve this step-by-step:
1. Let's assume the total number of animals in the pet shop is "x".
2. It is given that one-half (or 1/2) of the animals are dogs. So, the number of dogs would be (1/2) * x.
3. It is also given that one-fourth (or 1/4) of the animals are bunnies. So, the number of bunnies would be (1/4) * x.
4. It is mentioned that there are 6 cats in the pet shop.
5. Furthermore, it is mentioned that there is an equal number of cats and bunnies. Therefore, we can equate the number of cats (6) to the number of bunnies, which gives us (1/4) * x = 6.
6. To find the value of x, we can solve this equation:
(1/4) * x = 6
Multiplying both sides of the equation by 4:
x = 4 * 6
x = 24
7. Now, we can substitute the value of x back into the expression we found for the number of dogs:
number of dogs = (1/2) * x = (1/2) * 24 = 12
So, there are 12 dogs in the pet shop.
To find the number of dogs in the pet shop, let's first organize the information given:
- One-half of the animals are dogs.
- One-fourth of the animals are bunnies.
- Six animals are cats.
- There are an equal number of cats and bunnies.
Let's assign variables to unknown quantities:
Let "x" be the total number of animals in the shop, and "d" be the number of dogs.
From the information given, we can form equations:
1) Half of the animals are dogs: (1/2)x = d
2) One-fourth of the animals are bunnies: (1/4)x = d + b
3) There are an equal number of cats and bunnies: 6 = c = b (since 6 animals are cats)
Since there are an equal number of cats and bunnies, we can replace "c" with "b" in the equations.
Now, we have a system of equations:
1) (1/2)x = d
2) (1/4)x = d + b
3) b = 6
Let's solve the equations step by step:
From equation 3), we know b = 6.
Substituting b = 6 into equation 2), we get:
(1/4)x = d + 6
Now, let's isolate d:
(1/4)x - 6 = d
Finally, substitute this value of d into equation 1):
(1/2)x = (1/4)x - 6
Multiply the entire equation by 4 to eliminate the fractions:
2x = x - 24
Subtracting x from both sides:
x = -24
However, since the number of animals cannot be negative, this solution is not valid. It means there is no solution to the given set of information.