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29 July, 21:03

A mother is currently 7 times older than her son. In 3 years time, she will be 5 times older than her son. Let x and y be the present ages of the son and mother respectively.

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  1. 29 July, 21:38
    0
    Mother's present age: 42

    Son's present age: 7

    Step-by-step explanation:

    Let x represent the mother's age

    Let y represent the son's age

    The mother is currently seven times (*7) older than her son i. e.

    x = 7 * y

    x = 7y ... (eqn 1)

    In three years time i. e. the mother and son's age plus three (3)

    x + 3 and y + 3

    The mother will be 5 times (*5) older i. e.

    x + 3 = 5 * (y + 3)

    x + 3 = 5 (y + 3)

    x + 3 = 5y + 15

    Collect like terms

    x = 5y + 12 ... (eqn 2)

    Since x = 7y in eqn 1, we substitute x in eqn 2 i. e.

    7y = 5y + 12

    7y - 5y = 12

    2y = 12

    y = 6

    Since y=6, we substitute 6 in eqn 1

    x = 7y

    x = 7 * 6

    x = 42

    Hence, the present age of the mother and her son are 42 and 6 respectively.
  2. 30 July, 00:57
    0
    If the child is currently 6 years old and the mom is 42, in three years she'll be 45 and he'll be 9

    Step-by-step explanation:

    The son is y and the mom is x

    x=7y

    x+3=5 (y+3)

    7y+3=5y+15

    7y=5y+12

    2y=12

    y=6
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