# 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. minhkhue

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