The mean score of 5 students in a class is 60. If the highest score is 6 more than 3 times the lowest score, then what is maximum possible value of the range of the scores of 5 students?
Answers
91 ans is the answer
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Given : The mean score of 5 students in a class is 60.
the highest score is 6 more than 3 times the lowest score,
To Find : maximum possible value of the range of the scores of 5 students?
Solution:
The mean score of 5 students in a class is 60.
Hence total score = 5 * 60 = 300
Assume that lowest score is x
then Highest scores = 3x + 6
All other scores y
x ≤ y ≤ 3x + 6
Range = 3x + 6 - x = 2x + 6
Range will be maximum if x is max
as x + y₁ + y₂ + y₃ + 3x + 6 = 300
so Value of x will be maximum
if y₁ = y₂ = y₃ = x
Hence x + x + x + x + 3x+6 = 300
=> 7x = 294
=> x = 42
Range = 2x + 6 = 90
maximum possible value of the range of the scores of 5 students is 90
scores are
42 , 42 , 42 , 42 , 132
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