Finding More Cats than Dogs Based on Relationships

In a town, there is a unique relationship between the number of cats and dogs. When the number of cats increases by 5, the number of dogs decreases by 3. If the total number of cats and dogs is 50, how many more cats than dogs would there be if there were initially 20 cats?

Let C represent the number of cats and D represent the number of dogs. Starting with the equation:

$$ C + D = 50 $$

Given that the original number of cats is 20, we need to determine D when C is adjusted. After increasing cats by 5 and decreasing dogs by 3, the new equation would represent total animals:

$$ (C + 5) + (D - 3) = 50 $$

Finding the new relationship will help us answer the question.