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a set of five positive integers has a mean median and range of 7 how many distant sets whose members are listed from least to greatest could have these properties

  • math (?) -

    What properties?

  • math -

    a+b+c+d+e = 35 (mean=7)
    c = 7 (median)
    e = a+7 (range)

    a+b+7+d+a+7 = 35
    2a+b+d = 21

    If a=1, b+d=19
    But b<=7 and e=8
    1,b,7,d,8
    But, if b<=7, and d<=8, no go

    If a=2, b+d=17
    2,b,7,d,9
    same problem as above

    If a=3, b+d=15
    d<=10, so b>=5
    so we can have
    3,b,7,d,10 as
    3,5,7,10,10
    3,6,7,9,10
    3,7,7,8,10


    If a=4, b+d=13
    d <= 11, so b>=2. In fact, we know b>=4, so we can have
    4,b,7,d,11
    4,4,7,9,11
    4,5,7,8,11


    If a=5, b+d=11
    d<=12,
    5,b,7,d,12
    no go, since b>=5, meaning d<=6, but d must be at least 7.

    So, only the sets in boldface above are candidates.

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