Question

Team A and B love to play pickup basketball. There are no fouls and no three-pointers, so all shots are worth 2 points. The only problem is Team A always wins. They typically play games to 100 and Team B loses by 10 points. That is, the typical final score is Team A 100, Team B 90.

So, they decide to increase the point value of each basket for Team B to 2.2 points. Based on the typical results above, what effect is this most likely to have?

Team B will now tend to win by a margin of 1 point.

The teams will tend to score the exact same number of points.

Team A will still tend to win, by 1 point instead of 10.

Team B will now tend to win by 10 points.
Show your work.

Answer 1

Team A will still tend to win, by 1 point instead of 10.

Explanation:

New score of Team B:

90/2 × 2.2 = 99

Team A still wins, but by 1 point

Answer 2

The correct option is B) Team A will still tend to win, by 1 point instead of 10.

Explanation:

Consider the provided information.

There are no fouls and no three-pointers and all shots are worth 2 points.

The typical final score is Team A 100, Team B 90.

The final score of team A is 100, that means the number of shots by team A is 50 (50 × 2 = 100).

Similarly, the final score of team B is 90, that means the number of shots by team B is 45 (45 × 2 = 100).

They decide to increase the point value of each basket for Team B to 2.2 points.

Now, multiply 2.2 with 45.

45 × 2.2 = 99

Thus, the total score of team B is 99 and total score of team A is still 100. Therefore, team A will still tend to win, by 1 point.

Hence, the correct option is B) Team A will still tend to win, by 1 point instead of 10.