Question

The ratio of cats to dogs is 3 : 7.

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.

$\dfrac{3x}{7x-12}=\dfrac{3}{4}$

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

$12x=21x-36$

$12x-21x=-36$

$-9x=-36$

Divide both sides by -9.

$\dfrac{-9x}{-9}=\dfrac{-36}{-9}$

$x=4$

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.