SOLUTION: The age of three grand oaks totals exactly one thousand years. From the following information, determine the age of each tree. When the youngest tree has reached the age of the m

Let Y = the age of the youngest tree
Let M = the age of the middle tree
Let E = the age of the ELDEST tree.  

>>...The age of three grand oaks totals exactly one thousand years...<<

So

Y + M + E = 1000

That's the first equation.

>>...When the youngest tree has reached the age of the middle tree,...<<

The difference between the youngest and middle tree is M - Y

So M-Y is how many years will have passed when the youngest tree has 
reached the present age of the middle tree.

>>... the middle tree will be the age of the oldest tree...<<

So after those M-Y years, the middle tree will be E, the age of the 
Eldest.

So when we add M-Y to the middle tree's age, M, we get E.  Therefore

  M + (M-Y) = E     

That's the second equation.

>>...When the youngest tree has reached the age of the middle tree, 
the middle tree will be...four times the current age of the youngest 
tree...<<

 M + (M-Y) = 4Y

That's the third equation.

So we have this system of three equations in three unknowns

 Y + M + E = 1000
 M + (M-Y) = E
 M + (M-Y) = 4Y
 
which simplies to

 Y +  M + E = 1000
-Y + 2M - E = 0
-5 + 2M     = 0

I assume you can solve that system of equation.

Solution: Y = 133 years
          M = 333 years
          E = 533 years

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Checking:

The age of three grand oaks totals exactly one thousand years. 

133 + 333 + 533 = 1000

That checks.

>>...When the youngest tree has reached the age of the middle tree,...<<

That will take 200 years.

>>... the middle tree will be the age of the oldest tree...<<

That checks, because the eldest tree is 200 years older than the 

>>...and four times the current age of the youngest tree...<<

That checks because 4 times 133 is 533.

Edwin