Breeding mixed cats

Question
Is it possible to take a cat that is 1/2 one breed and 1/2 another breed, breed it with a purebred of one of those breeds,keep doing this with offspring and eventually end up with a purebred kitten?  If so, how many generations would this take?  

For example:  If I take a female cat who is half Bengal and half some other breed, and breed her to a Bengal, and then one of her kittens to a Bengal, and so on, would I eventually end up with a purebred Bengal?

Answer
Hi Bobbie
This is an unusual question but it has its base in genetics.
it will never become a full bengal because the kitten would be half bengal from one parent and 25% from the other ie 75%. The next kitten would be 87.5% bengal and each subsequent kitten would be exactly half the previous increase. This assumes the genetic take up of the kitten will remain constant, however nature being nature will throw a spanner in the works. So whilst it may be an idea it has no grounding in fact
Ray