SOLUTION: The combined ages of A and B are 48 years and A is twice as old as B was when A was half as old as B will be when B is three times as old as A was when A was three times as old a

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Question 1134603: The combined ages of A and B are 48 years and A is twice as old as B was when A
was half as old as B will be when B is three times as old as A was when A was
three times as old as B was then. how old is B?
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
Note: the answer posted before which is now deleted was in error.
Here is the correct solution:

Let x be the number of years in the past the first time.
Let y be the number of years in the future the second time.
Let z be the number of years in the past the third time. 

A+B=48
A = 2(B-x)
A-x = (1/2)(B+y)  
B+y = 3(A-z)
A-z = 3(B-z)

Those equations simplified and arranged in columns of like terms

  A +  B               = 48
  A - 2B + 2x          = 0
 2A -  B - 2x - y      = 0 
-3A +  B      + y + 3z = 0
  A - 3B          + 2z = 0

The solution by the augmented matrix method is

A=30, B=18, C=3, D=36, E=12.

Edwin
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