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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
Question
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?
in progress
0
Mathematics
3 years
2021-09-03T21:43:00+00:00
2021-09-03T21:43:00+00:00 1 Answers
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Answers ( )
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