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6 January, 19:03

Seven consecutive integers are added. The sum is 6 times the greatest of the seven integers. what is the smallest integer

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  1. 6 January, 19:25
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    the smallest integer is 15

    note that consecutive integers have a difference of 1 between them

    let the smallest integer be n

    then : n, n + 1, n + 2, n + 3, n + 4, n + 5, n + 6

    are seven consecutive integers with n + 6 being the largest, thus summing gives

    7n + 21 = 6 (6 + n)

    7n + 21 = 36 + 6n (distributing right side)

    7n - 6n + 21 = 36 (subtracting 6n from both sides)

    n + 21 = 36 ⇒ n = 36 - 21 = 15

    the smallest integer is 15
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