In a group of 60 workers, the average (arithmetic mean) salary is $80 a day per worker. if some of the workers earn $75 a day and all the rest earn $100 a day, how many workers earn $75 a day?

Let's let x = the number of workers making $75 per day
Then that would mean (60 - x) would be the number of workers who make $100 per day. 
Now the average salary, which needs to be 80, can be found by adding all the salaries of the 60 workers and dividing by 60.  The following equation can model this problem:
[75x + 100(60 - x)]/60 = 80  simplify the left side of the equation
(-25x + 6000)/60 = 80  multiply both sides by 60
-25x + 6000 = 4800  subtract 6000 from both sides
-25x = -1200  divide both sides by -25
x = 48  recall we set 'x' to equal the number of workers making $75 per day
And there you have it!  Hope this helps..