Sarah kept track of the points she scored during her first five basketball games in the table shown.
Game
1
2
3
4
5
Points Scored
8
12
10
6
14
What must she score during game 6 to have a mean of 12 points scored per game?
A. 10
B. 12
C. 14
D. 20
E. 22
To find the answer, we first need to find the total number of points Sarah has scored in the first five games. We can do this by adding up the points in each game: 8 + 12 + 10 + 6 + 14 = 50.
Next, we need to find the total number of games Sarah has played so far, which is 5.
The mean (average) score per game is calculated by dividing the total number of points by the total number of games: 50 / 5 = 10.
To find out what Sarah must score in game 6 to have a mean of 12 points scored per game, we need to take into account that the total score after game 6 will be the sum of the first five games' scores plus the score in game 6. Let's call the score in game 6 "x".
(50 + x) / (5 + 1) = 12
Simplifying the equation:
(50 + x) / 6 = 12
Multiplying both sides by 6:
50 + x = 72
Subtracting 50 from both sides:
x = 22
Therefore, Sarah must score 22 points in game 6 to have a mean of 12 points scored per game.
The correct answer is E. 22.
To find out what Sarah must score during game 6 to have a mean of 12 points scored per game, we need to find the sum of the points scored in the first five games and then divide it by the total number of games (which is 6 in this case).
Sum of points scored in the first five games = 8 + 12 + 10 + 6 + 14 = 50
Now, we can calculate the required score for game 6:
Total points required for 6 games = Mean points per game * Total number of games
Total points required for 6 games = 12 * 6 = 72
Therefore, Sarah must score 72 - 50 = 22 points during game 6 to have a mean of 12 points scored per game.
So the correct answer is E. 22.
To find the mean, you need to calculate the total number of points Sarah has scored in her first five games and then divide it by 5 (the number of games played).
Here's how you can calculate the mean:
1. Add up the points scored in each game: 8 + 12 + 10 + 6 + 14 = 50.
2. Divide the total points by the number of games played: 50 / 5 = 10.
To have a mean of 12 points per game, Sarah needs to score a total of 12 x 6 = 72 points in six games.
Since she has already scored 50 points in the first five games, the remaining number of points she needs to score in the sixth game can be calculated as follows:
Target points = Total points needed - Points already scored
Target points = 72 - 50 = 22
Therefore, Sarah needs to score 22 points in the sixth game to have a mean of 12 points scored per game.
The answer is option E.