Answer:
(D) 8.5
Step-by-step explanation:
We can consider the differences from the desired average that Alicia's scores are. She wants an average of 7, but has 3 scores of 6, so is a total of 3(6 -7) = -3 points from her desired average.
If her final quiz counts as two scores, she needs to have a score of x on that which will make her total deviation from average be 0.
-3 +2(x -7) = 0
x -7 = 1.5 . . . . . . add 3, divide by 2
x = 8.5 . . . . . . . add 7
Alicia needs an 8.5 on her final quiz to achieve an average of 7.
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Alternate solution
More conventionally, you would look at the total score Alicia needs. If she wants an average of 7 on 5 quizzes, she needs a total point count of ...
7 × 5 = 35
Her point count so far is ...
6 × 3 = 18
So, her final quiz must have an effective point count of ...
35 -18 = 17
Since it counts as 2 scores, it must be graded as ...
17/2 = 8.5 . . . score needed on her final quiz
With that score on her final, Alicia's average would be ...
(6 + 6 + 6 + 8.5 + 8.5)/5 = 35/5 = 7
