SOLUTION: The mean of 21 test score is 78. What mean score must three additional students acheive so that the mean for all 24 students is 80.
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Question 94916: The mean of 21 test score is 78. What mean score must three additional students acheive so that the mean for all 24 students is 80. Found 2 solutions by stanbon, Edwin McCravy:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The mean of 21 test scores is 78. What mean score must three additional students achieve so that the mean for all 24 students is 80.
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Let x be the mean of he three additional students.
EQUATION:
(21*78 + 3x)/24 = 80
21*78 + 3x = 1920
1638 + 3x = 1920
3x = 282
x = 94 (average needed on the last 3 tests)
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Cheers,
Stan H.
The mean of 21 test score is 78. What mean score must three
additional students acheive so that the mean for all 24
students is 80.
Let x = the mean score of the three additional students
We use this formula three times:
= , or
=
First we use it to find the sum of the scores when there
are 21 students, by substituting M=78 and N=21 and
solving for S:
= =
Mutiply both sides by 21
=
So, the sum of scores of the 21 is 1638
Second we use it to find the sum of the scores of the three
additional students, by substituting M=x and N=3 and
solving for S:
= =
Mutiply both sides by 3
=
So the sum of the scores of the 3 additional students is 3x.
Thirdly we use it to find the sum of the scores of all 24
additional students, by substituting M=80 and N=24 and
solving for S:
= =
Mutiply both sides by 24
=
S the sum of the scores of all 24 students
Now we form our equation from:
(Sum of scores of the 21) + (Sum of scores of the 3) = (Sum of scores of the 24)
1638 + 3x = 1920
Solve that and get x = 94. So the three additional students must
average 94.
Edwin
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