Question

Возраст трех могучих дубов в сумме составляет ровно 500 лет. Когда самый молодой из них достигнет нынешнего возраста среднего, средний дуб будет в том же возрасте, в котором находится старший и будет в четыре раза старше нынешнего возраста младшего дуба. Назовите нынешний возраст всех трех дубов.

Answer 1

Когда молодой будет в возрасте среднего, то средний - в возрасте старшего.
Это значит, что разность Средний - Молодой = Старший - Средний = a лет.
Пусть у молодого возраст x лет, тогда у среднего x+a лет, у старшего x+2a лет.
А вместе им 500 лет
x + x + a + x + 2a = 3x + 3a = 500
Когда молодой достигнет возраста среднего, а средний - старшего, то
средний (нынешний старший) будет в 4 раза старше нынешнего молодого.
4x = x + 2a
3x = 2a
Получаем систему
{ 3x + 3a = 500
{ 3x = 2a
Подставляем
2a + 3a = 5a = 500
a = 100 - это разница их возрастов.
3x + 3a = 3x + 300 = 500
3x = 200
x = 200/3 ~ 66,67 лет - это возраст младшего дуба.
x + a = 66,67 + 100 = 166,67 лет - это возраст среднего дуба
x + 2a = 66,67 + 200 = 266,67 лет - это возраст старшего дуба.

Answer 2

Calculation of the Ages of the Three Oak Trees

To determine the current ages of the three oak trees, let's break down the given information:

- The sum of the ages of the three oak trees is exactly 500 years. - 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 will be four times older than the current age of the youngest oak tree.

Let's denote the ages of the three oak trees as follows: - Age of the youngest oak tree: x years - Age of the middle oak tree: y years - Age of the oldest oak tree: z years

Based on the given information, we can set up 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 and will be four times older than the current age of the youngest oak tree: - (x + y) / 2 = z - z = 4x

Now, let's solve these equations to find the ages of the three oak trees.

Solving the Equations

From equation 2, we can substitute z with 4x: - (x + y) / 2 = 4x

Simplifying the equation: - x + y = 8x - y = 7x

Substituting y = 7x into equation 1: - x + 7x + z = 500 - 8x + z = 500

Substituting z = 4x: - 8x + 4x = 500 - 12x = 500 - x = 41.67

Since the ages of the oak trees are typically whole numbers, we can round x to the nearest whole number: - x ≈ 42 years

Now, we can find the ages of the other oak trees: - y = 7x ≈ 7 * 42 ≈ 294 years - z = 4x ≈ 4 * 42 ≈ 168 years

Current Ages of the Three Oak Trees

Based on the calculations, the current ages of the three oak trees are approximately: - The youngest oak tree: 42 years - The middle oak tree: 294 years - The oldest oak tree: 168 years

Please note that these ages are approximate values based on the given information and the rounding of the youngest oak tree's age.