Sunday, October 9, 2011

Age Problem 7 Solution

This is the solution to a algebra age word problem as asked by a anonymous user: "Nona is one-third as old as her mother. Five years ago, she was only one-fifth of the age of her mother. How old is Nona now? "

It is easier to set this up with two unknowns say x and y and have 2 equations.

The 1st equation would be:  x = 1/3(y)  or x = y/3   since Nona is currently 1/3 as old as her mother.  Now 5 years ago she was only 1/5th the mothers age so the other equation would be..

x -5 = 1/5(y - 5)   multiply by 5..

5x - 25 = y - 5 so

y = 5x - 20  .. plug this back into the 1st equation and you get..

x = (5x - 20)/3  - -multiply by 3

3x = 5x - 20  so 2x = 20  and x = 10

So Nona is 10 years old currently and the mom is 30.   To check this go 5 years back... Nona would be 5 and the mother would be 25   ------   5/25 = 1/5ths of her mothers age...

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