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.
[tex]\dfrac{3x}{7x-12}=\dfrac{3}{4}[/tex]
[tex]4(3x)=3(7x-12)[/tex]
[tex]12x=21x-36[/tex]
[tex]12x-21x=-36[/tex]
[tex]-9x=-36[/tex]
Divide both sides by -9.
[tex]\dfrac{-9x}{-9}=\dfrac{-36}{-9}[/tex]
[tex]x=4[/tex]
Now, the total number of animals at the beginning is
[tex]Total=3x+7x[/tex]
[tex]Total=10x[/tex]
[tex]Total=10(4)[/tex]
[tex]Total=40[/tex]
Therefore, the total number of animals at the beginning is 40.
