SOLUTION: The average of Ed's ten test scores is 87. The teacher throws out the top and bottom scores, which are 55 and 95. What is the average of the remaining set of scores?

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Question 49434: The average of Ed's ten test scores is 87. The teacher throws out the top and bottom scores, which are 55 and 95. What is the average of the remaining set of scores?
Answer by Born2TeachMath(20) About Me  (Show Source):
You can put this solution on YOUR website!
This problem uses the idea of finding the average of a bunch of numbers, and then works the problem backwards.
The problems starts by saying that the average of Ed's 10 test scores is 87. We know we have 10 scores, and the average is 87.
Therefore:
Cross multiply, we have: score1+score2+score3+score4+score5+score6+score7+score8+score9+score10 = 87*10 = 870
Now, we need to remove his scores of 55 and 95. We don't know which tests they are, but we don't need to, either.
So, take any two out from both sides (say score1 and score 10 - it doesn't make any difference)
score2+score3+score4+score5+score6+score7+score8+score9 = 870 - 55 - 95
score2+score3+score4+score5+score6+score7+score8+score9 = 720
So Ed's 8 remaining test scores add to 720.
So now we need to find the average of the rest of the scores, which there are 10 - 2 = 8 remaining.
Using the average equation again: %28score2%2Bscore3%2Bscore4%2Bscore5%2Bscore6%2Bscore7%2Bscore8%2Bscore9%29%2F8+=+average
And we know that the eight remaining scores add to 720, so 720%2F8+=+average
So Ed's average is 90!