Question

Коля увлекается нумизматикай .Если разложить Колины монеты в стопки по 22 монеты то останется 8 монет. Сколько монет останется если разложить монеты в стопки по 11 монет в каждой? Обоснуйте свой ответ.Пожалуйста как для 5 заранее спасибо!!!

Answer 1

Останется 8 монет, а количество стопок увеличится в два раза. Из 8 монет стопку в 11 монет не получить.

Answer 2

Problem Analysis

Kolya has a collection of coins and wants to know how many coins will be left if he arranges them in stacks of 11 coins each. We know that if he arranges them in stacks of 22 coins, there will be 8 coins left. We need to determine the number of coins that will be left when arranged in stacks of 11 coins each.

Solution

To solve this problem, we can use the concept of modular arithmetic. The remainder when dividing the total number of coins by 11 will give us the number of coins left.

Let's denote the total number of coins as 'N'. We know that when the coins are arranged in stacks of 22, there are 8 coins left. This can be represented as:

N % 22 = 8

Now, we need to find the number of coins left when arranged in stacks of 11. This can be represented as:

N % 11 = ?

To find the value of N % 11, we can substitute the value of N % 22 from the previous equation:

N % 11 = (22 * k + 8) % 11

where 'k' is an integer.

Simplifying the equation:

N % 11 = (2 * 11 * k + 8) % 11 = (8) % 11 = 8

Therefore, when the coins are arranged in stacks of 11, there will be 8 coins left.

Conclusion

When Kolya arranges his coins in stacks of 11, there will be 8 coins left. This conclusion is based on the fact that when the coins are arranged in stacks of 22, there are 8 coins left