SOLUTION: translate to variable expression and solve. if mary is 24 years old. mary is twice as old as Ann was, when Mary was as old as Ann is now. How old is Ann.

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Question 661745: translate to variable expression and solve.
if mary is 24 years old. 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(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Mary is 24 years old.  
Let Ann be A years old. 

Mary is twice as old as Ann was x years ago, which was (A - x). 
Also x years ago, Mary was (24 - x), and that is how old Ann is now,
which is A. 

x years ago, Mary was 24 - x
x years ago, Ann was A - x

So the equations comes from:

         %28matrix%283%2C1%2C%0D%0A%0D%0A%22Mary%27s%22%2C+age%2C+now%29%29 = 2·%28matrix%285%2C1%2C%0D%0A%0D%0A%22Ann%27s%22%2C+age%2C+x%2C+years%2C+ago%29%29

and

         %28matrix%285%2C1%2C%0D%0A%0D%0A%22Mary%27s%22%2C+age%2C+x%2Cyears%2C+ago%29%29 = %28matrix%283%2C1%2C%0D%0A%0D%0A%22Ann%27s%22%2C+age%2C+now%29%29

So the system of equations is

                24 = 2(A - x)
                24 - x = A

Solve that system and get x = 6 and A = 18.

So 6 years ago Ann was 12 and Mary is twice that now.

Edwin