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8 April, 22:09

Five years ago, Tom was one third as old as his father was then. In 5 years, Tom will be half as old as his father will be then. Find their ages now. Show your equation

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  1. 8 April, 23:22
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    The father is 35years old and the son Tom is 15years old

    Step-by-step explanation:

    Let the father's be y

    Let Tom's age be T

    5 years ago:

    The father's age is: y - 5

    Tom's age:

    T - 5.

    But Tom's age was one third the father's age. This is written as:

    T - 5 = 1/3 (y - 5)

    3 (T - 5) = y - 5

    3T - 15 = y - 5

    3T - y = - 5 + 15

    3T - y = 10 (1)

    In 5years time:

    The father's age is:

    y + 5

    Tom's age:

    T + 5

    But in 5years time, Tom will be half as old as his father. This is written as:

    T + 5 = 1/2 (y + 5)

    2 (T + 5) = y + 5

    2T + 10 = y + 5

    2T - y = 5 - 10

    2T - y = - 5 (2)

    Therefore, the equations are

    3T - y = 10 (1)

    2T - y = - 5. (2)

    Solving by elimination method:

    Subtract equation (2) from (1)

    3T - y = 10

    - (2T - y = - 5)

    T = 15

    Substituting the value of T into equation (1)

    3T - y = 10

    3 (15) - y = 10

    45 - y = 10

    45 - 10 = y

    y = 35

    Therefore,

    The father is 35years old and the son Tom is 15years old
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