With these scooters, you are better off taking the carb off, clean it completely and make sure you put everything back together the way it was before- they're senstive.
Then slash your gas line and put in a lawnmower filter. That'll save a whole lot of headache. I had my QT50 running well for over a year since I did that.
Before then, without the lawnmower filter, I had to work on the carb like every 5-6 months and that was annoying.
Also, in addition, the petcock is supposed to have a fine screen between the petcock nut and the petcock itself. '88 models and older moped probably has screens that are totally gone by now. A sink screen would work well. Brass is a better metal screen and lasts a very very long time.
Extreme rust in the gas tank is my biggest complaint with the QT 50.