Let's call the number of hamburgers sold "H" and the number of cheeseburgers sold "C". We know that:
C = 3H (the number of cheeseburgers sold was three times the number of hamburgers sold)
We also know that the total number of hamburgers and cheeseburgers sold was 412:
H + C = 412
Now we can substitute the first equation into the second equation to get an equation with only one variable:
H + 3H = 412
4H = 412
H = 103
Therefore, 103 hamburgers were sold on Friday.