Mark wants to improve his free throw percentage in basketball. He has shot 1250 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 has shot 100 free throws for the day.

x = 15, y = 5

Step-by-step explanation:

x + y = 20   The number of days equals 20

50x + 100y = 1250    The free throws per day add up to 1250

Solve by substituion:

rewrite the first equation to get the value for x

x = -y +20  Subsstitute for x in the second equation

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

-50y + 1000 + 100y = 1250  Subtract 1000 from both sides and simplify y

50y = 250 Divide both sides by 50

y = 5

substitute in the first equation and solve for x

x + 5 = 20

x = 15

Substitute into the second equation to check

50(15) + 100(5) = 1250

750 + 500 = 1250

1250 = 1250   True

And just for illustration, the attachment shows the graph of the solution, (15,5)