SOLUTION: In a math class with 20 students, the grades on a recent quiz ranged from 0 to 10, inclusive. The average grade of the first 12 quiz papers the teacher marked was 7.5. If x is

Question 1043134: In a math class with 20 students, the grades on a recent quiz ranged from 0 to 10, inclusive. The average grade of the first 12 quiz papers the teacher marked was 7.5. If x is the average grade for the class on this quiz, then which of the following could be the possible grade range?
A) 4 ≤ x ≤ 8.5 .
B) 4 ≤ x ≤ 7.5
C) 3.5 ≤ x ≤ 7.5
D) 5 ≤ x ≤ 8.50
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
We have the average for 12 of the 20 students which is 7.5
The maximum total of scores is 12 * 7.5 + 8 * 10
90 + 80 = 170
So the maximum possible average is 170/20 = 8.5
Now let's find the minimum possible average.
90 + 8 * 0 = 90
90/20 = 4.5, which is the minimum possible average.
So one could write 4.5 <= x <= 8.50
Only answer D is consistent with this.
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