Question

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. Formulate and solve a system of equations to determine how many times Mark shot 100 free throws for the day.

Answer 1

Mark shot 100 free throws for 5 days.

Explanation:

Let x represent number of days when Mark shots 50 free throws and y represent number of days when Mark shots 100 free throws.

We have been given that Mark has shot 1,250 free throws over the last 20 days. We can represent this information in an equation as:

`x+y=20...(1)`

`x=20-y...(1)`

We are also told that Mark shot either 50 or 100 free throws a day and shot a total of 1250 free throws. We can represent this information in an equation as:

`50x+100y=1250...(2)`

Upon substituting equation (1) in equation (2), we will get:

`50(20-y)+100y=1250`

`1000-50y+100y=1250`

`1000+50y=1250`

`1000-1000+50y=1250-1000`

`50y=250`

`(50y)/(50)=(250)/(50)`

`y=5`

Therefore, Mark shot 100 free throws for 5 days.