Can you provide an algebraic solution?

Question

The age of 3 grand oaks totals exactly 1000 years. From the following information, determine the age of each tree. When the youngest tree has reached the age of the middle tree, the middle tree will be the age of the oldest tree and four times the current age of the youngest tree.

Answer 1

Well, I started on this, and got stumped halfway along. Let's see if it comes to me while I type all this nonsense out.

y= age of youngest tree

m= age of middle tree

o= age of oldest tree

y+m+o = 1000

"the middle tree will be the age of the oldest tree and four times the current age of the youngest tree"

From this we can state that the oldest tree IS currently four times the age of the youngest tree

so

o=4y

and

y+4y+m = 1000

5y+m = 1000

"When the youngest tree has reached the age of the middle tree, the middle tree will be the age of the oldest tree"

From this we can gather that the age of the middle tree is exactly halfway between the ages of the oldest and youngest trees (or the mean)

So we can find a value for m in terms of y

m= (o+y)/2

   = (4y+y)/2

   = (5y)/2

   = 5y/2

Gods, am I making sense so far? I hope so.

Right, so we can say

y + 4y + 5y/2 = 1000

2y + 8y+ 5y = 2000

15y = 2000

y = 133.33....

o = 4y = 4 x 133.33333...

o = = 533.33.....

m = (o-y)/2 + y

    = (533.33...-133.33...)/2 + 133.33....

    = 400/2 + 133.33....

    = 333.33.......

333.33...+ 133.33...+ 533.33... = 1000

Phew.

You MAY want to tidy all that up a bit.