Question

У Пифагора однажды спросили, сколько у него учеников. «Половина моих учеников изучает прекрасную математику, четверть исследует тайны природы, седьмая часть упражняет силу духа. Добавьте ещё к ним трёх юношей, из коих Теон – самый способный». Сколько учеников было у Пифагора?

Answer 1

Всего учеников Х
Х/2 математики
Х/4 природоведы
Х/7 йоги
вычитаем из Х всех учеников получаем 3
Х-Х/2-Х/4-Х/7=3
3Х/28=3
Х=28

Answer 2

Number of Pythagoras' Students

According to the information provided, Pythagoras had students who were divided into different categories based on their areas of study.

Pythagoras stated that half of his students studied mathematics, a quarter explored the secrets of nature, and one-seventh practiced spiritual strength. Additionally, he mentioned that there were three more young men, with Theon being the most capable among them.

To determine the total number of Pythagoras' students, we can use the given fractions and the additional information about the three young men.

Let's break down the fractions mentioned:

- Half of the students studied mathematics: This means that half of the total number of students is dedicated to studying mathematics. - A quarter explored the secrets of nature: This indicates that a quarter of the total number of students is involved in studying the secrets of nature. - One-seventh practiced spiritual strength: This implies that one-seventh of the total number of students is focused on practicing spiritual strength.

To find the common denominator for these fractions, we need to find the least common multiple (LCM) of 2, 4, and 7, which is 28.

Now, let's calculate the number of students in each category:

- Mathematics: Half of the students, which is 14 out of 28 students. - Secrets of nature: A quarter of the students, which is 7 out of 28 students. - Spiritual strength: One-seventh of the students, which is 4 out of 28 students. - Additional three young men: This adds 3 more students to the total count.

To find the total number of students, we add up the students in each category and the additional three young men:

14 (mathematics) + 7 (secrets of nature) + 4 (spiritual strength) + 3 (additional young men) = 28 students.

Therefore, Pythagoras had a total of 28 students.