SOLUTION: Twelve students took a math exam and obtained an average score of 80%. If four students received an A grade (a score of 90% or above), then what was the minimum possible percentage

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Question 1095098: Twelve students took a math exam and obtained an average score of 80%. If four students received an A grade (a score of 90% or above), then what was the minimum possible percentage mean score of the other students?
Found 3 solutions by josmiceli, greenestamps, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +S+ = the sum of the scores of the 12 students
+80+=+S%2F12+
+S+=+960+
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The smallest possible score of the other students ( not A's )
happens when each of the A students gets 100%
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+4%2A100+=+400+
and
+960+-+400+=+560+
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So, there are +12+-+4+=+8+ students who didn't get A's and
Let +x+ = their minimum possible mean % score
+x+=+560+%2F+8+
+x+=+70+
70% is the answer
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Get a 2nd opinion if needed

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!

Josgarithmetic said get a second opinion.... Her answer is fine; but I would solve the problem differently....

If we are looking for the minimum average of the other 8 students, then we want the 4 students who got A's to get the highest possible score, which I will assume is 100.

Let's talk scores out of 100 instead of percentages, to make the description easier....

The average is 80, and 4 students each scored 100. That is a total of 4*20=80 points above what is needed to make an average of 80. That means the average for the other 8 students must be such that their total scores are 80 below the overall average of 80. 80 points, divided equally among the 8 students, is 10 points each. So the average of the other 8 students is 10 points below the overall average of 80; 80-10 = 70.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
greenestamps, I did not give any solution response to this posted question. I did not try to solve this posted question. Please adjust your solution post, since I did not ask for a second opinion here.