Question

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.

Answer 1

Answer: 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)

Answer 2

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 day