SOLUTION: A teacher wants to calculate the average score of her students. She has the scores of 20 students, but she accidentally misplaced one score. If the average of the remaining 19 scor

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Question 1204991: A teacher wants to calculate the average score of her students. She has the scores of 20 students, but she accidentally misplaced one score. If the average of the remaining 19 scores is 85, what should be the misplaced score to maintain a weighted mean of 87?
Found 3 solutions by josgarithmetic, mananth, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
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125

Teacher forgot to use some x.
19 students had average of 85 but for all 20 students, the real average was 87.

%28x%2B19%2A85%29%2F20=87

x%2B19%2A85=20%2A87

x=20%2A87-19%2A85

x=125

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
A teacher wants to calculate the average score of her students. She has the scores of 20 students, but she accidentally misplaced one score. If the average of the remaining 19 scores is 85, what should be the misplaced score to maintain a weighted mean of 87?
The average of the 19 students is 85 as calculated by teacher
So total score = 19*85 =1615
Let the misplace score be x
Total score of 20 students will be 1615+x
The average is 87
The average now is (1615+x)/20= 87
1615+x = 87*20
1615+x= 1740
x = 1740-1615
x =125

The misplaced score is 125 to maintain a mean of 87.
CHECK
1615+125 =1740
1740/20=87

Answer by greenestamps(13198) About Me  (Show Source):
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A quick informal solution using logical reasoning, if formal algebra is not required.

The 19 scores she has are, on average, 87-85 = 2 points short of the desired mean; so together they are 19*2 = 38 points short. That means the missing score must be 38 points above the desired mean.

ANSWER: 87+38 = 125