Question

Mr. Sarpy went to shoot some hoops on the basketball court. For every shot that he made within the three-point line he earned 2 points and every shot he made behind the three-point line he earned 3 points. Mr. Sarpy shot a total of 50 shots and earned a total of 115 points. Write a system of equations that best models x, the number of 2 point shots, and y, the number of 3 point shots.

Answer 1

x + y = 50 (1) and 2x + 3y = 115 (2); x = 35, y = 15

Explanation:

Since x represents the number of 2 point shots and y represents the number of 3 point shots. If the total number of shots is 50, then x + y = 50 (1)

Also, the total 2 point shots is number of 2 point shots × points per shot = 2x and the total 3 point shots is number of 3 point shots × points per shot = 3y. Since the total number of points is 115, then

2x + 3y = 115 (2)

So, the system of equations are

x + y = 50 (1) and 2x + 3y = 115 (2)

We can solve for x and y by substituting x = 50 - y into (2)

So, 2(50 - y) + 3y = 115

100 - 2y + 3y = 115

100 + y = 115

y = 115 - 100

y = 15

So, x = 50 - y

= 50 - 15

= 35