Question

У бабушки 10 внуков,и все они имеют различные возраста. Алексей - самый старший из них. Однажды бабушка посчитала, что сумма возрастов всех её внуках равна 180 (все возрасты целые числа). Какое наименьшее возраст может иметь Алексей? помогите с объяснением ​

Answer 1

Ответ:

23 года Алексею

Пошаговое объяснение:

Если Алексей старший и возраст всех внуков разный, то сумма

13+14+15.......+22=175 это самые большие возраста в порядке убывания с 22

Значит Алексею может быть только 23 года

Answer 2

Problem Analysis

We are given that a grandmother has 10 grandchildren, all with different ages. Alexey is the oldest among them. The grandmother calculated that the sum of all her grandchildren's ages is equal to 180, and all ages are whole numbers. We need to determine the minimum age Alexey can have.

Solution

To find the minimum age Alexey can have, we need to consider the ages of the other grandchildren. Since all the ages are different, we can assume that the other 9 grandchildren have ages ranging from 1 to 9. This is because if any of them had an age greater than 9, the sum of their ages would exceed 180.

Let's calculate the sum of the ages of the other 9 grandchildren from 1 to 9: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

Now, we can subtract this sum from 180 to find the minimum age Alexey can have: 180 - 45 = 135

Therefore, the minimum age Alexey can have is 135.

Explanation

The minimum age Alexey can have is 135 because if we assume the other 9 grandchildren have ages ranging from 1 to 9, the sum of their ages would be 45. Subtracting this sum from the total sum of all the grandchildren's ages (180) gives us 135 as the minimum age for Alexey.

Example

Let's consider an example to illustrate this:

If we assume the ages of the other 9 grandchildren are as follows: 1, 2, 3, 4, 5, 6, 7, 8, 9

The sum of their ages would be: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

Subtracting this sum from the total sum of all the grandchildren's ages (180) gives us: 180 - 45 = 135

Therefore, the minimum age Alexey can have is 135.

Conclusion

The minimum age Alexey can have is 135, assuming the other 9 grandchildren have ages ranging from 1 to 9.