Question
A set contains twelve numbers. The average of the first
eight numbers is (y - 3), and the average of the last three numbers is (y + 5). The average of the entire set is 'y'. If the 9th number of the set is 45, then find the value of 'y'.Solution
Sum of the numbers of the set = 12y. Sum of first 8 numbers = 8(y - 3) = 8y - 24. Sum of last 3 numbers = 3(y + 5) = 3y + 15. Including the 9th number, the total sum is 8y - 24 + 45 + 3y + 15 = 11y + 36. Equating this to the total sum, 11y + 36 = 12y. Solving for y, y = 36. Therefore, the correct value of y is 36.
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