Question

В классе 25 учеников а сумма их возрастов составляет 270 лет.Найдутся ли в классе 20 учащихся сумма возрастов которых больше 260 лет? а найдется б ненайдется

Answer 1

Нет ненайдёться никогда

Answer 2

Problem Analysis

We are given a class with 25 students, and the sum of their ages is 270 years. We need to determine if there are 20 students in the class whose sum of ages is greater than 260 years.

Solution

To solve this problem, we can use a combination of mathematical reasoning and trial and error.

Let's assume that there are 20 students in the class whose sum of ages is greater than 260 years. We can represent the ages of these 20 students as variables, such as x1, x2, x3, ..., x20.

According to the problem statement, the sum of the ages of these 20 students should be greater than 260 years. Mathematically, we can express this as:

x1 + x2 + x3 + ... + x20 > 260

Since we know that the sum of the ages of all 25 students is 270 years, we can express this as:

x1 + x2 + x3 + ... + x20 + x21 + x22 + x23 + x24 + x25 = 270

Now, we can subtract the second equation from the first equation to eliminate the variables for the remaining 5 students:

(x1 + x2 + x3 + ... + x20) - (x21 + x22 + x23 + x24 + x25) > 260 - 270

Simplifying further:

x1 + x2 + x3 + ... + x20 - x21 - x22 - x23 - x24 - x25 > -10

Since the sum of the ages of the remaining 5 students cannot be negative, we can conclude that:

x1 + x2 + x3 + ... + x20 > -10

Therefore, if there are 20 students in the class whose sum of ages is greater than 260 years, the sum of their ages should be greater than -10. However, this condition is always true since the sum of ages cannot be negative.

Therefore, we can conclude that there will always be 20 students in the class whose sum of ages is greater than 260 years.

Answer

Yes, there will always be 20 students in the class whose sum of ages is greater than 260 years.