A black snake lies at the base of an apple tree and a cat is climbing in the tree branches. The number of apples on the tree is four less than twice the tree's height. One year ago the the cat's age was one-third of his mother's current age. Two years from now twice the cat's mother's age will be four less than the current length of the snake. Three years from now the cat will be two-thirds as old as its mother is at that time. If the length of the snake is 2 more than the height of the tree, then how many apples are on the tree?

32

31

25

To solve this problem, let's break it down step by step:

1. Let's assume the height of the tree is "x". So, "2x - 4" is the number of apples on the tree. (Given: "The number of apples on the tree is four less than twice the tree's height.")

2. The length of the snake is "x + 2". (Given: "The length of the snake is 2 more than the height of the tree.")

3. Let's assume the current age of the cat is "c" and the current age of the cat's mother is "m".

4. One year ago, the cat's age was "c - 1" and his mother's age was "m - 1". (Given: "One year ago, the cat's age was one-third of his mother's current age.")

5. Two years from now, twice the cat's mother's age will be "2(m + 2)" and the current length of the snake is "x + 2", so we can set up the equation: "2(m + 2) = x + 2 - 4". Simplifying this equation gives us "2m + 4 = x - 2".

6. Three years from now, the cat's age will be "c + 3" and his mother's age will be "m + 3". (Given: "Three years from now, the cat will be two-thirds as old as its mother is at that time.")

Now, we have a system of equations:

Equation 1: 2x - 4 = the number of apples on the tree
Equation 2: x + 2 = the length of the snake
Equation 3: c - 1 = (1/3)(m)
Equation 4: 2m + 4 = x - 2
Equation 5: c + 3 = (2/3)(m + 3)

To find the number of apples on the tree, we need to solve this system of equations.