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24 October, 15:26

Daniel, my son, is exactly one fifth of my age. in 21 years time, i will be exactly twice his age. my wife is exactly seven times older than my daughter, jessica. in 8 years time, my wife will be three times older than jessica. how old are daniel and jessica now?

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  1. 24 October, 15:28
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    Let daniel's age = d and let jessica's age = j

    let your current age = x and your wife's current age = y

    x = 5d (given in question)

    ∴ x - 5d = 0

    x + 21 = 2 (d+21) (given in question)

    ∴ x + 21 = 2d + 42

    ∴ x - 2d = 21

    We can solve these two rearranged equations simultaneously by multiplying the first equation by - 1 and adding them. This gives us the following:

    3d = 21

    ∴ d = 7

    This means that daniel is currently 7 and (if we substitute d = 7 into one of the equations) you are 35. We use a similar method for your wife's and jessica's current ages.

    y = 7j (given in question)

    ∴ y - 7j = 0

    y + 8 = 3 (j + 8)

    ∴y + 8 = 3j + 24

    ∴ y - 3j = 16

    If we use a similar method of elimination we get this:

    4j = 16

    ∴ j = 4

    Hence, from this we can concur that daniel is 7 and jessica is 4.
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