Question

Всем ученикам одного 5-го класса было предложено принять участие в одной из следующих олимпиад: по математике, по русскому языку и по труду. После проверки работ выяснилось, что половина учеников этого класса участвовали в олимпиаде по математике, четверть - по русскому языку, седьмая часть - по труду и ещё три лентяя не участвовали ни в одной из олимпиад. Сколько человек учиться в этом классе?

Answer 1

1)1-1/2-1/4-1/7=28/28-14/28-7/28-4/28=3/28- часть учеников, не участвующих не  в одной олимпиаде
2)3/(3/28)=28-учеников в классе
Ответ:28 учеников

Answer 2

Problem Analysis

We are given that all the students in a 5th-grade class were offered to participate in one of the following Olympiads: mathematics, Russian language, or labor. After checking the papers, it was found that half of the students participated in the mathematics Olympiad, a quarter participated in the Russian language Olympiad, and one-seventh participated in the labor Olympiad. Additionally, three students did not participate in any of the Olympiads. We need to determine the total number of students in the class.

Solution

Let's assume the total number of students in the class is x.

According to the given information: - Half of the students participated in the mathematics Olympiad, which is x/2 students. - A quarter of the students participated in the Russian language Olympiad, which is x/4 students. - One-seventh of the students participated in the labor Olympiad, which is x/7 students. - Three students did not participate in any of the Olympiads.

To find the total number of students, we can add up the number of students who participated in each Olympiad and the number of students who did not participate:

x/2 + x/4 + x/7 + 3 = x

Now, we can solve this equation to find the value of x.

Calculation

Let's solve the equation to find the value of x:

x/2 + x/4 + x/7 + 3 = x

To simplify the equation, we can find a common denominator for the fractions:

7x/14 + 3x/14 + 2x/14 + 3 = x

Combining the fractions:

(7x + 3x + 2x)/14 + 3 = x

Simplifying the numerator:

12x/14 + 3 = x

Multiplying both sides of the equation by 14 to eliminate the denominator:

12x + 42 = 14x

Subtracting 12x from both sides:

42 = 2x

Dividing both sides by 2:

x = 21

Answer

There are 21 students in this class.