Question
Average of nine consecutive numbers is 55. Find the sum
of the smallest and largest number.Solution
Let the numbers be (b - 4), (b - 3), (b - 2), (b - 1), b, (b + 1), (b + 2), (b + 3), and (b + 4). The average of these numbers is (b - 4 + b - 3 + b - 2 + b - 1 + b + b + 1 + b + 2 + b + 3 + b + 4) / 9 = 55. Simplifying, (9b) / 9 = 55, so b = 55. The sum of the smallest and largest numbers is (b - 4) + (b + 4) = b + b = 2b = 2 x 55 = 110.
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