1

Problem

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?

2

Step

Let’s represent the highest score as x.

3

Step

The average score of 8 players in a basketball game is

14.5 points

4

Step

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

12 points

5

Step

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

\$8 \times 14.5\$ = 116

6

Step

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

\$7 \times 12\$ = 84

7

Step

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

8

Solution

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

9

Sumup

Please summarize steps

Choices

10

Choice-A

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

Wrong 20

11

Choice-B

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

Wrong 24

12

Choice-C

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

Correct 32

13

Choice-D

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

Wrong 36

14

Answer

Option

C

15

Sumup

Please summarize choices