SOLUTION: Two years ago my age was three times the square of my son's age. In three years time my age will be four times my son's age. Find my son's age. When will his age be one-third of mi

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Question 624839: Two years ago my age was three times the square of my son's age. In three years time my age will be four times my son's age. Find my son's age. When will his age be one-third of mine?
Answer by lwsshak3(11628) About Me  (Show Source):
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Two years ago my age was three times the square of my son's age. In three years time my age will be four times my son's age. Find my son's age. When will his age be one-third of mine?
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2 years ago:
son's age=x
father's age=3x^2
..
In 3 years: (5 years from 2 years ago)
son's age=x+5
father's age=3x^2+5
Equation: 3x^2+5=4(x+5)=4x+20
3x^2+5=4x+20
3x^2-4x-15=0
(3x+5)(x-3)=0
3x+5=0
x=-5/3 (reject, x>0)
or
x-3=0
x=3
son's present age=x+2=5
fathers's present age=3x^2+2=29
..
When son's age 1/3 of father's:
let x= years from 2 years ago:
(3+x)/(27+x)=1/3
9+3x=27+x
2x=18
x=9
son's age 1/3 of father's: 9 years from 2 years ago or 7 years from the present