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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

  • Math -

    "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

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