Engine backfires when accelerating, idles rough but runs fine over 50+ miles per hour.

Idle is rough because not a right Air/ Gas mixture.
The ideal air /gas ratio is 14.6:1. If less than that it has rich mixture. If it more then that it has a lean mixture.
Back fire happens when accelerated because of of rich mixture pumped out at exhaust cycle is burning.
At speed above 40 miles/hour, temperature and fast compression cycle make the problem is less obvious.
Cheap first shot is to replace the air filter to correct this ratio. If it doesn't help, need Fuel distributor service. ( However people like to make easy money from you first, they will convince you for a turn up) Good Luck. I'll check back to see how the progress going.