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is younger than Tom, but older than Harry. Their ages in years are consecutive odd integers. 's mother is three times as old as , and she is also 13 years older than twice as old as Tom. How old are Harry, , and Tom

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  1. H < D < T

    H + 2 = D ... D + 2 = T

    3 D = 2 T + 13

    3 D = 2 (D + 2) + 13 = 2 D + 17

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  2. D = 's age

    T = Tom's age

    H = Harry's age

    M = Mother's age

    D < T

    D > H

    D = T - 2 Add 2 to both sides

    D + 2 = T - 2 + 2

    D + 2 = T

    T = D + 2

    M = 3 D

    also:

    M = 2 T + 13 = 2 ( D + 2 ) + 13 = 2 * D + 2 * 2 + 13 = 2 D + 4 + 13 = 2 D + 17

    M = M

    3 D = 2 D + 17 Subtract 2 D to both sides

    3 D - 2 D = 2 D + 17 - 2 D

    D = 17 yrs

    T = D + 2 = 17 + 2 = 19 yrs

    D = H + 2 Subtract 2 to both sides

    D - 2 = H + 2 - 2

    D - 2 = H

    H = D - 2

    H = 17 - 2 = 15 yrs

    Proof:

    's mother is three times as old as :

    M = 3 D = 3 * 17 = 51 yrs

    's mother is 13 years older than twice as old as Tom:

    M = 2 T + 13 = 2 * 19 + 13 = 38 + 13 = 51 yrs

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