SOLUTION: Mary is 24. Mary is twice as old as Ann was, when Mary was as old as Ann is now. How old is Ann?

Question 574661: Mary is 24.
Mary is twice as old as Ann was, when Mary was as old as Ann
is now.
How old is Ann?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
Mary is 24.
Mary is twice as old as Ann was, when Mary was as old as Ann
is now.
How old is Ann?

Let A = Ann's age now
Let y = the number of years ago it was when Mary was Ann's present age, or A.

Then y years ago, Mary was 24-y and she was also A, so we set those equal:

       24-y = A 

Also y years ago, Ann was A-y, and Mary's age now, 24, is twice this, so

         24 = 2(A-y) 

So that is the system of equations:



Solve that system by substitution and get A = 18 and y=6

Answer: Ann is 18.

Checking:  Ann is now 18. Mary is now 24, so 6 years ago Mary was 18, which
is Ann's age now.  That checks.  6 years ago Ann was 12.  Since Mary's age now
is 24, she is indeed twice as old as Ann was 6 years ago.  So the answer is correct.

Edwin

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