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?

and in four years time his age doubled and increased

by 10 will match his mother’s age. How old is Jon

now?

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