Question

У бабусі 10 онуків. усі онуки різного віку. іринка-найстарша. якщо додати роки усіх онуків, отримаємо 180.скільки найменше років може мати іринка?

Answer 1

1) 180:10=18 (р) Ірині.

Answer 2

Problem Analysis

We are given that a grandmother has 10 grandchildren of different ages, and the sum of their ages is 180. We need to determine the minimum age that the oldest grandchild, Irinka, can be.

Solution

Let's assume that Irinka is the oldest grandchild and her age is x. Since the sum of all the grandchildren's ages is 180, we can set up the following equation:

x + (age of the second grandchild) + (age of the third grandchild) + ... + (age of the tenth grandchild) = 180

Since all the grandchildren have different ages, we can assume that the ages of the other grandchildren are in increasing order. Let's represent the ages of the other grandchildren as a sequence of numbers: a1, a2, a3, ..., a9.

The equation can now be rewritten as:

x + a1 + a2 + a3 + ... + a9 = 180

We know that Irinka is the oldest grandchild, so her age must be greater than or equal to the ages of the other grandchildren. Therefore, we can set up the following inequality:

x >= a1, x >= a2, x >= a3, ..., x >= a9

To find the minimum age of Irinka, we need to find the minimum value of x that satisfies the equation and the inequality.

Let's consider the extreme case where all the other grandchildren have the minimum possible ages. In this case, the ages of the other grandchildren would be 1, 2, 3, ..., 9. Substituting these values into the equation, we get:

x + 1 + 2 + 3 + ... + 9 = 180

Simplifying the equation, we get:

x + 45 = 180

Subtracting 45 from both sides, we get:

x = 180 - 45 = 135

Therefore, the minimum age that Irinka can have is 135 years.

Answer

The minimum age that Irinka can have is 135 years.