Question

At a basketball game, a team made 55 successful shots. They were a combination of 1- and 2-point

shots. The team scored 94 points in all. Write and solve a system of equations to find the number of
each type of shot.
There were 37 2-point shots and 18 1-point shots.

Answer 1

By solving a system of linear equations, we find that the basketball team made 39 2-point shots and 16 1-point shots, not 37 and 18 as the student originally thought.

Step-by-step explanation:

To solve for the number of 1-point shots and 2-point shots in a basketball game where a team made 55 successful shots for a total of 94 points, we set up a system of equations. Let's designate x as the number of 2-point shots and y as the number of 1-point shots. The first equation represents the total shots made:

• x + y = 55

The second equation represents the total points scored:

• 2x + y = 94

To solve the system, we can use the substitution or elimination method. If we multiply the first equation by -1 and add the two equations, we eliminate y:

• -x - y = -55
• 2x + y = 94
• -----------
• x = 39

Now that we have the value for x, we can substitute it into either equation to find y:

• 39 + y = 55
• y = 55 - 39
• y = 16

Therefore, there were 39 2-point shots and 16 1-point shots. Note that the answer provided by the student was incorrect: they stated there were 37 2-point shots and 18 1-point shots when in reality there were 39 2-point shots and 16 1-point shots.