The four members of a team are comparing scores on the Individual
Test. Amy scored 3 points less and Brad scored 6 points less than the average of the team members, while Cara scored 5 points more than the average. Don scored 28 points. What was the score of the highest-scoring member of this team?
nine total points below average , so nine total above
Don scored four points above average
... Cara outscored him by one point ... 29
x = average
A = Amy's points = x - 3
B = Brad's points = x - 6
C = Cara's points = x + 5
D = Don 's points = 28
Average:
x = ( A + B + C + D ) / 4
Put members of a team points in this equation.
x = ( x - 3 + x - 6 + x + 5 + 28 ) / 4
x = ( 3 x + 24 ) / 4
Multiply both sides by 4
4 x = 3 x + 24
Subtract 3 x to both sides
4 x - 3 x = 3 x + 24 - 3 x
x = 24
A = Amy's points = x - 3 = 24 - 3 = 21
B = Brad's points = x - 6 = 24 - 6 = 18
C = Cara's points = x + 5 = 24 + 5 = 29
D = Don 's points = 28
Cara scored most points, 29.
To find the score of the highest-scoring member of the team, we need to determine the scores of each member first.
Let's denote the average score of the team members as A. We know that:
Amy's score = A - 3
Brad's score = A - 6
Cara's score = A + 5
Don's score = 28
We can create an equation using these scores:
(Amy's score) + (Brad's score) + (Cara's score) + (Don's score) = 4A
(A - 3) + (A - 6) + (A + 5) + 28 = 4A
By simplifying the equation:
3A + 24 = 4A
24 = 4A - 3A
24 = A
So, the average score A is 24.
Now we can substitute the value of A back into the original equations to find the individual scores:
Amy's score = 24 - 3 = 21
Brad's score = 24 - 6 = 18
Cara's score = 24 + 5 = 29
Don's score is already given as 28.
Therefore, the highest-scoring member of the team is Cara, with a score of 29.