Question

At a basketball game, a team made 53 successful shots. They were a combination of 1- and

2-point shots. The team scored 90 points in all. Write and solve a system of equations to find the
number of each type of shot.
There were
2-point shots and 1-point shots.

Answer 1

Let x be the number of 1 point shots, and y be the number of 2 point shots.

So the system is:

x+y=53

1x+2y=90

We can solve this system by substitution.

x+y=53, x=53-y

x+2y=90

53-y+2y=90

53+y=90

y=37

That means, the team made 37 two point shots.

If the team made 37 two point shots, the team scored 37 x 2, or 74 points from 2 point shots, meaning that it made 16 one point shots.

So the correct answer is: 16 one point shots, 37 two point shots.

Let me know if this helps!