A local hamburger shop sold a combined total of 637 hamburgers and cheeseburgers on Saturday. There were 63 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?

Let x be the number of hamburgers sold.

Therefore, the number of cheeseburgers sold is x - 63.

The total number of hamburgers and cheeseburgers sold is x + (x - 63) = 2x - 63, which is equal to 637.

So, 2x - 63 = 637
2x = 700
x = 350

Therefore, 350 hamburgers were sold on Saturday.