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anudiv · Feb 26, 2010, 11:41 PM

Five years ago a woman's age was the square of her son's age.Ten years hence,her age will be twice that of her son's age.Find:
1.the age of the son five years ago.
2.the present age of the woman.

ROLCAM · Feb 27, 2010, 01:26 AM

1.the age of the son five years ago.*** his age 5
2.the present age of the woman.*** her age now 30

Unknown008 · Feb 27, 2010, 08:31 AM

Let the age of the son be s and that of the woman be w, at present.

So, the age of the son to the square will give the age of the woman, both five years ago, therefore, squaring the age of the son should give the age of the woman.

$(s-5)^2 = (w-5)$

Then, 10 years from now, the age of the woman will be twice that of the son, so, if you multiply the age of the son by two, his age should be the same as the woman:

$2(s+10) = (w+10)$

You have two equations with two unknowns. You can solve them by simultaneous equations.

$(s-5)^2 = (w-5)$

$2(s+10) = (w+10)$

Expand the first one:

$s^2 - 10 s + 25 = w-5$

Make w the subject:

$s^2 - 10 s + 30 = w$ ... a

Make w the subject of formula of the second equation above:

$2(s+10) = (w+10)$

$2s+10= w$ ... b

Now equate a and b.

$s^2 - 10 s + 30 = 2s+10$

Solve for s to get the son's present age and remove 5 from that to get his age 5 years ago. You'll get two answers and obviously, one will be wrong. You'll know which is wrong if you get a negative answer for the age of the son five years ago.

From there, you can find the age of the woman five years ago but squaring the answer for 1. and get her present age.

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