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23 August, 20:19

Mrs. Tiwari has two sons, one being exactly one year older than the other. Her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the ages of her sons.

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  1. 23 August, 23:58
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    Let

    x = child number 1

    y = son number 2

    z = Mrs. Tiwari

    We have then:

    y = x + 1

    z = x ^ 2 + y ^ 2

    z + 4 = 5 (y+4)

    We solve the system:

    Equation1

    y = x + 1

    Equations 1 and 2:

    z = x ^ 2 + (x + 1) ^ 2

    z = x ^ 2 + x ^ 2 + 2x + 1

    z = 2x ^ 2 + 2x + 1

    Equation 2 and 3

    z + 4 = 5 (y+4)

    2x ^ 2 + 2x + 1 + 4 = 5 (x + 1 + 4)

    2x ^ 2 + 2x + 5 = 5x + 25

    2x ^ 2 + 2x - 5x + 5 - 25 = 0

    2x ^ 2-3x - 20 = 0

    x = 4

    Substituting:

    y = x + 1

    y = 4 + 1

    y = 5

    answer:

    the ages of her sons are

    x = 4

    y = 5
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