Question

Один человек имел 102 монеты. Он поровну разделил их между двумя своими детьми. Каждому досталось по 12 монет и одна осталась лишней. Какая система счисления использовалась и сколько было монет?Решите пожалуйста очень подробно.

Answer 1

Пусть х - основание системы счисления
Составляем уравнение
1*x^2+2 = 2*(1*x+2)+1
x^2 - 2x + 2-4-1 = 0
x^2 - 2x - 3 = 0
корни 3 и -1 

Значит х = 3 (больше 0)

Answer 2

Problem Analysis

We are given that a person had 102 coins and divided them equally between their two children. Each child received 12 coins, and there was one coin left over. We need to determine the number system used and the total number of coins.

Solution

Let's analyze the problem step by step:

1. The person had 102 coins. 2. The coins were divided equally between two children. 3. Each child received 12 coins. 4. There was one coin left over.

To find the number system used, we can analyze the number of coins each child received. If each child received 12 coins, and there was one coin left over, it suggests that the number system used is base 12. In base 12, the digits range from 0 to 11, and when counting, after reaching 11, the next number is represented as 10.

Now, let's calculate the total number of coins:

1. Each child received 12 coins. 2. There was one coin left over.

To find the total number of coins, we can multiply the number of coins each child received by 2 (since there are two children) and add the one extra coin:

Total number of coins = (12 * 2) + 1 = 24 + 1 = 25 coins.

Therefore, the person had a total of 25 coins.

To summarize: - The number system used is base 12. - The person had a total of 25 coins.

Please let me know if I can help you with anything else.