Question
In a classroom, the average score of 15 students on a
test is 44 points. If 5 new students, each with an average score of 'x' points, join the class, and 8 students, each with an average score of '(x – 6)' points, leave the class, the new average score of the 12 remaining students becomes '(x – 1)' points. What is the total score of these 12 students?Solution
ATQ, The sum of the score of 15 students on a test is = 44 × 15 = 660 The sum of the the score of 5 students is = 5 × a = 5a The sum of the score of 8 students is = 8(a – 6) = (8a – 48) The sum of the score of 12 students is = 12(a – 1) = (12a – 12) According to the question, 660 + 5a – (8a – 48) = 12a – 12 660 + 5a – 8a + 48 = 12a – 12 660 + 48 + 12 = 12a + 3a 720 = 15a a = 48 a = 48 Average score of 12 students is = 48 – 1 = 47 The sum of the score of 12 students is = 47 × 12 = 564
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