Question

Пифагор на вопрос о числе учеников, посещающих его школу, ответил по преданию, так" половина учеников изучают математику, четверть- музыку, а седьмая часть пребывает в молчании и, кроме того, есть ещё три женщины". Сколько было учеников у Пифагора?

Answer 1

Пусть число учеников это - x. Составим и решим уравнение: 

x-(1/2 + 1/4 + 1/7)x= 3
x= 3/(1-(14 + 7 + 4)/28) = 3 * 28/3 = 289(уч.)

Ответ: У Пифагора было 28 учеников.

Answer 2

Calculating the Number of Students at Pythagoras' School

According to the legend, Pythagoras responded to a question about the number of students attending his school by stating that half of the students studied mathematics, a quarter studied music, a seventh were silent, and there were three women. To calculate the total number of students, we can use this information.

Step 1: Calculate the Fraction of Students Studying Mathematics, Music, and Remaining Silent - Half of the students studied mathematics - A quarter studied music - A seventh were silent

Step 2: Calculate the Total Number of Students - Add the fractions together and account for the three women mentioned in the response.

Let's proceed with the calculations.

Calculation

- Half of the students studied mathematics: 1/2 - A quarter studied music: 1/4 - A seventh were silent: 1/7 - Total number of students: x

The equation can be set up as: 1/2x + 1/4x + 1/7x + 3 = x

Solving for x: 1/2x + 1/4x + 1/7x + 3 = x (7/14)x + (3/14)x + (2/14)x + 3 = x (12/14)x + 3 = x 12x + 42 = 14x 42 = 2x x = 21

Answer: According to the legend, there were 21 students at Pythagoras' school.