Get us a pic of your cart.
Sounds like this cart just needs going through with a really good tune up. And air box will need to be completely sealed. Bungy cords work great if the tabs are completely broken: run one over the center and hook underneath. Just be mindful of the clutch. Probably should pull fuel pump, tear it apart, and clean also. Check and replace fuel lines if needed. Be sure to get the exact same size!! Check the line going to the back of the engine also. The cart will never run right if it is leaking. It's what helps operate the fuel pump with vacuum. Most backfires on 4 stroke Yamaha's is due to the throttle on the carb not closing all the way when you let off the pedal. You probably need to adjust the valves on this cart also.
But get us some pic's of your cart and we'll let you know what you have.
And welcome to the forum.