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find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer

asked by Roy
  1. "find three consecutive even intergers"
    Let M be the middle integer.
    The three numbers are M-2, M, M+2

    "the sum of the first two integers is greater than 9 more than the third integer"
    (M-2 + M) > M+2 + 9
    on solving
    M > 13

    "sum of the first and third integers is less than 17 more than the second integer"
    M-2 + M+2 < M+17
    on solving
    M < 17

    That leaves us with two choices,
    M=14, or M=16.

    Check:
    M=14
    12+14=26 > 16+9=25 OK
    12+16=28 < 14+17=31 OK

    M=16
    14+16=30 > 18+9=27 OK
    14+18=32 < 16+17=33 OK

    So there are two valid solutions,
    12,14,16 or 14,16,18

    posted by MathMate

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