Mark wants to improve his free throw percentage in basketball he has shot 1,250 free throws over the last 20 days. he shot either 50 or 100 free throws a day. during the 20 day period, how many times did mark shoot 100 free throws for the day?

Let's use a for number of days when he shot 50 shots and b for number of days when he shot 100 shots.
We have:
a + b = 20

We also know that he shot total of 1250 shots:
50a + 100 b = 1250

We have two equations. We can solve them for a and b.  Let's rearange first equation for a:
a= 20 - b
We insert this into second equation:
50 * (20 - b ) + 100b = 1250
1000 - 50b + 100b = 1250
50b = 250
b = 5
a = 20 - 5
a = 15

Mark shot 100 shots on 5 days.