Question

In the garden of a witch there are 30 animals: dogs, cats and mice. The witch turns 6

dogs into cats. Then she turns 5 cats into mice. Now her garden has the same number of
dogs, cats and mice. How many cats were there at the beginning?​

Answer 1

Answer:

There were 16 dogs, 9 cats and 5 mice at the beginning.

Step-by-step explanation:

let number of dogs = a,

number of cats = b,

and number of mice = c

The witch turns 6 dogs into cats.

now, number of dogs = a-6

number of cats = b+6

and number of mice = c

Then, she turns 5 cats into mice.

now, number of dogs = a-6

number of cats = b+6-5 = b+1

and number of mice = c+5

Now her garden has the same number of

dogs, cats and mice.

so,

a-6 = b+1 = c+5

from this,

a = c+5+6 = c+11 ----(1)

b = c+5-1 = c+4 ----(2)

given, total number of animals = 30

=> a+b+c = 30

=> c+11+c+4+c = 30 (putting a and b from (1) and (2))

=> 3c+15 = 30

=> 3c = 30-15 = 15

=> c = 15/3 = 5 mice

=> a = c+11 = 5+11 = 16 dogs

=> b = c+4 = 5+4 = 9 cats

Answer 2

Answer:

9 cats

Step-by-step explanation: