10 Six years ago Jon was one-sixth the age of his mother and in four years time his age doubled and increased by 10 will match his

10 Six years ago Jon was one-sixth the age of his mother
and in four years time his age doubled and increased
by 10 will match his mother’s age. How old is Jon
now?​

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  1. Answer:

    Jon is 11 years old

    Step-by-step explanation:

    We write the following equations describing the sentences of the problem, using the letter M to represent Jon’s mom’s current age, and j to represent his current age.

    First sentence: “Six years ago Jon was one-sixth the age of his mother.”

    translates into:

    J – 6 = (M – 6) / 6

    Second sentence: “in four years time his age doubled and increased

    by 10 will match his mother’s age.”

    2 * (J + 4) + 10 = M + 4   which removing parentheses gives: 2 J + 18 = M + 4

    We solve for “M” in the first equation

    6 (J – 6) = M – 6

    6 J – 36 = M – 6

    M = 6 J – 30

    and now use this result to substitute for M in the second equation

    2 J + 18 = (6 J – 30) + 4

    and work on solving for J

    2 J + 18 = 6 J – 30 + 4

    18 + 26 = 6 J – 2 J

    44 = 4 J

    J = 44 / 4

    J = 11

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