A local hamburger shop sold a combined total of 589 hamburgers and cheeseburgers on Friday. There were 61 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Friday?
Let X be the number of hamburgers sold on Friday.
The number of cheeseburgers sold on Friday is X - 61.
So the total of hamburgers and cheeseburgers sold is X + X - 61 = 2X - 61 = 589.
Thus 2X = 589 + 61 = 650.
Therefore X = 650 / 2 = <<650/2=325>>325 hamburgers. Answer: \boxed{325}.