Question

The ratio of cats to dogs is 3 : 7.

12 dogs escaped and the ratio is now 3 : 4.
Work out how many animals there were at the beginning.

Answer 1

Given:

The ratio of cats to dogs is 3:7.

12 dogs escaped and the ratio is now 3 : 4.

To find:

The total number of animal at the beginning.

Solution:

Let the number of cats and dogs at the beginning are 3x and 7x respectively.

12 dogs escaped. So, the remaining number of dogs is (7x-12).

New ratio of cats and dogs is 3:4.

`(3x)/(7x-12)=(3)/(4)`

`4(3x)=3(7x-12)`

`12x=21x-36`

`12x-21x=-36`

`-9x=-36`

Divide both sides by -9.

`(-9x)/(-9)=(-36)/(-9)`

`x=4`

Now, the total number of animals at the beginning is

`Total=3x+7x`

`Total=10x`

`Total=10(4)`

`Total=40`

Therefore, the total number of animals at the beginning is 40.