Question

В двух классах, 6а и 6б, вместе 82 ученика. Известно, то мальчиков в этих классах поровну. Мальчики в 6а составляют 3/5 учащихся своего класса, а мальчики 6б составляют 4/7 учащихся своего класса. Сколько учащихся в каждом из этих классов?

Answer 1

В 6а x учеников, из них мальчиков 3x/5. 
В 6б y учеников, из них мальчиков 4y/7.
Всего в обоих классах 82 ученика
x + y = 82
Количество мальчиков в классах одинаковое
3x/5 = 4y/7
Из 2 уравнения
21x = 20y
Значит, y = 21x/20
x + 21x/20 = (20x + 21x)/20 = 41x/20 = 82
x = 40 - в 6а
y = 21*40/20 = 42 - в 6б.

Answer 2

Calculating the Number of Students in Each Class

To solve this problem, we can use a system of equations to represent the given information and solve for the number of students in each class.

Let's denote: - x as the number of boys in class 6a - y as the number of boys in class 6b

Given: - The total number of students in both classes is 82, so the total number of boys is half of that, which is 41. - The boys in class 6a make up 3/5 of the total students in the class. - The boys in class 6b make up 4/7 of the total students in the class.

We can represent this information in the following equations: 1. x + (1 - 3/5)x = 41 (for class 6a) 2. y + (1 - 4/7)y = 41 (for class 6b)

Solving the Equations

Let's solve these equations to find the values of x and y.

1. For class 6a: - x + (2/5)x = 41 - (7/5)x = 41 - x = 41 * (5/7) - x = 29.2857

2. For class 6b: - y + (3/7)y = 41 - (10/7)y = 41 - y = 41 * (7/10) - y = 28.7

Conclusion

Based on the given information, we have found that the number of students in each class is approximately: - Class 6a: 29 students - Class 6b: 29 students