The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?

Let’s denote the highest score as x:

The mean score of 8 players in a basketball game is

14.5 points

The highest individual score is removed, the mean score of the remaining 7 players becomes

12 points

Calculate total points:
The total points scored by all 8 players is

\$8 \times 14.5\$ = 116

Calculate total points without the highest score:
The total points scored by the remaining 7 players is

\$7 \times 12\$ = 84

Find the highest score:
The highest score (x) is the difference between the total points scored by all 8 players and the total points scored by the remaining 7 players

x = 116 - 84

x = 32

So, the solution is that the highest score was 32 points.

If the highest score were 20 points, then the total points scored by all 8 players would be \$8 \times 20 = 160\$. However, this contradicts the given mean score of 14.5 points for all 8 players

20

If the highest score were 24 points, then the total points scored by all 8 players would be \$8 \times 24 = 192\$. Again, this contradicts the given mean score of 14.5 points for all 8 players

24

As we’ve calculated previously if the highest score were 32 points, then the total points scored by all 8 players would be \$8 \times 32 = 256\$. This fits with the given mean score of 14.5 points for all 8 players, satisfying the conditions of the problem

32

If the highest score were 36 points, then the total points scored by all 8 players would be \$8 \times 36 = 288\$. This also contradicts the given mean score of 14.5 points for all 8 players

36

Option

C

Can you summarize what you’ve understood in the above steps?