Congrats on the Cadet 80 find. I don't know if they are rare or not. The 80 is newer than the 70 and 100. I believe it came out in 1977 and used a Briggs and Stratton engine. They are called Lawn Tractors, not Garden tractors, and Cadets, not Cub Cadets. The Cadets have their own set of mowers, front blades, and snowthrowers specific to the Cadet. Hope you get her running.
Under edit: Guess I type to slow, LOL.