tough question?

Question

A woman is currently 21 years older than her daughter. Eleven years before the current time, the daughter was two- thirds as old as her mother. What is the age of the mother?

Answer 1

Not that tough!

 

First set up a variable.  Let's call x the daughter's age now.

 

That means that the mother's age is x + 21.

 

11 years ago, the daughter's age was x - 11.  And the mother's age was (x + 21) - 11 = x + 10

 

At that time (11 years ago), the daughter's age was 2/3 of her mother's.  That means that x - 11 = (2/3) (x + 10)

 

Now you have an equation you can solve:

x - 11 = (2/3) (x + 10)

 

Let's multiply both sides by 3 to get rid of the fraction:

3(x - 11) = 2 (x + 10)

3x - 33 = 2x + 20

x -33 = 20

x = 53

 

So the daughter's age is now 53, and the mother is 21 years older, so she's 74.  That's the answer.

 

 

To check...

 

11 years ago the daughter was 53 - 11, or 42.  And the mother was 74 - 11, or 63.

 

And indeed, 42 is 2/3 of 63!  So the answer is correct.