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We know that the woman has 21 pets which are either a cat or a bird and the total number of legs is 76.

We know that a cat has 4 legs and a bird has 2 feet

So we assume that all pets are cats
If this is so the total number of legs would be 4*21=84

The difference between the number of feet the bird and cat has is 2

In order to get the number of gets the expression would be:
 \frac{84-76}{4-2} = \frac{8}{2} =4

Therefore there are 4 birds and 21-4=17 cats.