SOLUTION: The score for half students in a class on a certain test was 90.The score for another four of the students was 84. If the average ( arithmetic mean) score for all of the students w

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Question 551640: The score for half students in a class on a certain test was 90.The score for another four of the students was 84. If the average ( arithmetic mean) score for all of the students was 82,what was the average score for the remaining students?
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Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
THE PROBLEM AS WRITTEN
There is not enough information to solve the problem as written. We do not know how many students are "the remaining students."
If there were 10 students in the class, there would be one remaining student whose grade was 34.
5%2A90%2B4%2A84%2B1%2Ax=10%2A82 --> x=450%2B336%2Bx=820 --> x=820-450-336=34
If there were 16 students in the class, there would be 4 remaining students with an average score of 64.
8%2A90%2B4%2A84%2B4%2Ax=16%2A82 --> 720%2B336%2B4x=1312 --> 4x=1312-720-336=256 --> x=256%2F4=64
If there were 88 students in the class, the remaining 44 students had an average score of 73.
44%2A90%2B4%2A84%2B40%2Ax=88%2A82 --> 3960%2B336%2B40x=7216 --> 40x=7216-3960-336=2920 --> x=2920%2F40=73
A PROBLEM THAT CAN BE SOLVED
If the problem said "The score for another one fourth of the students was 84," we would write
%281%2F2%2990%2B%281%2F4%2984%2B%281%2F4%29x=82, and solve for x.
Multiplying both sides of the equation times 4 we get rid of the fractions/denominators, and the rest is easy.
2%2A90%2B84%2Bx=4%2A82 --> 180%2B84%2Bx=328 --> x=328-180-84=64