Question

На каникулах две третьих учеников класса ходили в кино а три седьмых - посетили выставку.Сколько учащихся в классе, если их меньше 40?

Answer 1

Т. к. 2/3, то кол-во учеников делится на 3, иначе в кино ходило нецелое число учеников.
Т. к. 3/7, то кол-во учеников делится на 7, иначе посещало выставку нецелое число учеников.
Наименьшее число, делящееся на 3 и 7, равно 3*7=21.
Если больше 21, то как минимум 42, что больше 40.
Ответ: 21. 

Answer 2

Problem Analysis

We are given that two-thirds of the students in a class went to the cinema during the holidays, and three-sevenths of the students visited an exhibition. We need to determine the total number of students in the class if there are fewer than 40 students.

Solution

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

According to the given information: - Two-thirds of the students went to the cinema, which means (2/3)x students went to the cinema. - Three-sevenths of the students visited an exhibition, which means (3/7)x students visited the exhibition.

The total number of students who went to the cinema and visited the exhibition is the sum of these two quantities: (2/3)x + (3/7)x

We are also given that the total number of students is less than 40, so we can set up the following inequality: (2/3)x + (3/7)x < 40

To solve this inequality, we can multiply both sides by the least common multiple (LCM) of the denominators, which is 21: 21 * (2/3)x + 21 * (3/7)x < 21 * 40

Simplifying the inequality: 14x + 9x < 840 23x < 840

Dividing both sides by 23: x < 36.52

Since the number of students must be a whole number, the maximum possible value for x is 36.

Therefore, the total number of students in the class is 36.

Answer

If there are fewer than 40 students in the class, the total number of students is 36.