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It sounds like either the engine is hurt or the carbs have issues. I would suggest doing a compression test on all 3 cylinders. I suspect you are going to find one is significantly lower than the other 2. You are looking mainly for consistency, and they should be somewhere around 110 psi per cylinder. Remember to leave the other 2 spark plugs installed when you are doing the test. Also, ground out the spark plug leads so the engine doesn't start while doing the compression test. While you pull out each spark plug, make a mental note of what it looks like, especially the color of the tip of the plug. Again, you want to see consistency. If you have one that is darker or lighter than the other, it could indicate a problem with that carb.
Although the price seems tempting, this could potentially turn into a money pit. It really depends on what is wrong with it. There are references available to get retail values on skis as well.
Another point to consider is whether you are capable of doing the work yourself or if you are going to have to pay someone else to do the work. If you cannot do the work yourself, I would advise to steer clear of this one.