Yamaha YFM 225 Moto-4 History and Help....
Pretty much a predacessor to the Big Bear if anything. In 86 or 87, they had your 225 and the moto-4 YFM350 which looked almost identical. Also there was the 350 Big Bear and they all were very similar in looks. Just a bunch of utility quads. They upped the 225 to a 250 in 88 I think and still sold it up into the mid 90's. I think they dropped it shortly after the Timberwolf arrived.
Your carb may need a rebuild, and I would check out the fuel lines and tank to make sure they aren't full of crap. We sold ours probably 6-7 years ago. My grandpa has an 87 that still runs (barely). Poor thing has been massively abused, and has sat out in the rain for almost all of its life. Exhaust is almost rusted off, brakes don't work, plastic is dry rotted and the racks are all bent up, but by some act of god it still starts and runs.
For a quad that old, if yours still looks in good shape physically, then it will probably run just fine with a few easy fixers such as carb work.