Question

Помогите решитьВозраст трёх дубов составляет ровно 500 лет. Когда самый молодой из этих дубов достигнет нынешнего возраста среднего, средний дуб будет в том же возрасте, в котором сейчас находится старший, и будет в четыре раза старше нынешнего возраста самого младшего дуба. Назовите нынешний возраст всех трёх дубов.

Answer 1

Х+у+z=500
y-x=z-y
z=4x
***********
х+у+4x=500
y-x=4x-y
z=4x
***********
х+у+4x=500
2y=5x
z=4x
***********
х+5x/2+4x=500
y=5x/2
z=4x
***********
x*15/2=500
y=5x/2
z=4x
***********
x=66,(6)
y=166,(6)
z=266,(6)

Answer 2

Problem Analysis

We are given that the combined age of three oak trees is exactly 500 years. We are also given that when the youngest oak tree reaches the current average age, the average oak tree will be the same age as the oldest oak tree, and it will be four times older than the current age of the youngest oak tree. We need to determine the current age of all three oak trees.

Solution

Let's assume the current ages of the three oak trees are x, y, and z years, respectively.

From the given information, we can form the following equations:

1. The sum of the ages of the three oak trees is 500 years: x + y + z = 500

2. When the youngest oak tree reaches the current average age, the average oak tree will be the same age as the oldest oak tree: (x + y + z) / 3 = z

3. The average oak tree will be four times older than the current age of the youngest oak tree: (x + y + z) / 3 = 4x

We can solve these equations simultaneously to find the values of x, y, and z.

Solving the Equations

Let's solve the equations using substitution:

From equation 2, we have: z = (x + y + z) / 3

Multiplying both sides by 3, we get: 3z = x + y + z

Rearranging the terms, we have: x + y = 2z [Equation 4]

Substituting equation 4 into equation 1, we have: 2z + z = 500

Simplifying, we get: 3z = 500

Dividing both sides by 3, we get: z = 500 / 3

Therefore, the current age of the oldest oak tree (z) is approximately 166.67 years.

Substituting z into equation 4, we have: x + y = 2 * 166.67

Simplifying, we get: x + y = 333.34 [Equation 5]

Substituting z into equation 3, we have: (166.67 + x + y) / 3 = 4x

Multiplying both sides by 3, we get: 166.67 + x + y = 12x

Rearranging the terms, we have: 11x - x + y = 166.67

Simplifying, we get: 10x + y = 166.67 [Equation 6]

Now we have two equations (equations 5 and 6) with two variables (x and y). We can solve these equations simultaneously to find the values of x and y.

Subtracting equation 5 from equation 6, we have: (10x + y) - (x + y) = 166.67 - 333.34

Simplifying, we get: 9x = -166.67

Dividing both sides by 9, we get: x = -166.67 / 9

Therefore, the current age of the youngest oak tree (x) is approximately -18.52 years.

Substituting x into equation 5, we have: -18.52 + y = 333.34

Simplifying, we get: y = 333.34 + 18.52

Therefore, the current age of the middle oak tree (y) is approximately 351.86 years.

Answer

Based on the given information, the current ages of the three oak trees are approximately: - The youngest oak tree: -18.52 years - The middle oak tree: 351.86 years - The oldest oak tree: 166.67 years

Please note that the negative age for the youngest oak tree is not realistic and may indicate an error in the problem statement or calculations.