The average score of 51 girls in a class is 309. If the average score of the first 26 girls is 305 and that of the last 26 girls is 314, what is the score of the girl at the middle number?
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Let the number of boys be 3x and the number of girls be x.
Then, total number of students = 4x
Average score of the class = A
∴ Total score of all the students = 4Ax
Average score of all the boys = A + 1
∴ Total score of all the boys = 3x (A + 1) = 3Ax + 3x
⇒ Total score of all the girls = 4Ax - 3Ax - 3x = Ax - 3x = (A - 3)x
⇒ Average score of the girls = x(A−3)x=(A−3)
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