SOLUTION: six student write an exam.the average score obtained on the exam by the group of students is 71% if the first two students each obtained a mark of 73% while the next three students
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Question 1195129: six student write an exam.the average score obtained on the exam by the group of students is 71% if the first two students each obtained a mark of 73% while the next three students each obtain a mark of 68% what was the mark obtained by the sixth student?
(1) A standard solution method, using the standard method of calculating averages....
2 scores of 73, plus 3 scores of 68, plus 1 score of x, makes an average of 71:
ANSWER: 76
(2) An alternative method that keeps the numbers in the calculations smaller, which can be used in any problem like this where the numbers are all close together....
Compare each number to the average and look at the "overs" and "unders". The average is obtained only if the overs and unders are equal.
2 scores of 73, each 2 over the average: +4
3 scores of 68, each 3 under the average: -9
The balance with those 5 scores is (+4)+(-9) = -5; that means the 6th score must be +5.
