To solve this problem, let's assume the current ages of the three redwood trees are:
Youngest tree: x years old
Middle tree: y years old
Oldest tree: z years old
According to the given information, the sum of the ages of the three trees is 1000 years:
x + y + z = 1000 --(1)
We also know that when the youngest tree (x) reaches the age of the middle tree (y), the middle tree will have reached the age of the oldest tree (z):
x + y = z --(2)
Furthermore, at that time (when the youngest tree reaches the age of the middle tree), the middle tree will be four times the current age of the youngest tree:
y = 4x --(3)
Now, we have a system of three equations (1), (2), and (3), which we can solve simultaneously.
To solve this system of equations, we can start by substituting the value of y from equation (3) into equations (1) and (2).
From equation (3), we have:
y = 4x
Substituting y = 4x into equation (1):
x + 4x + z = 1000
Simplifying, we get:
5x + z = 1000 --(4)
Substituting y = 4x into equation (2):
x + 4x = z
Simplifying, we get:
5x = z --(5)
Now, we have two equations (4) and (5) with two variables (x and z). We can solve for their values.
Let's rearrange equation (5) to get z in terms of x:
z = 5x
Substituting this into equation (4):
5x + 5x = 1000
Combining like terms, we get:
10x = 1000
Dividing both sides by 10, we find:
x = 100
Now that we have the value of x, we can find the values of y and z.
From equation (3):
y = 4x
y = 4 * 100
y = 400
From equation (5):
z = 5x
z = 5 * 100
z = 500
Therefore, the current ages of the three redwood trees are:
Youngest tree: 100 years old
Middle tree: 400 years old
Oldest tree: 500 years old