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.