Question

У нашій школі три шості класи. У 6 - А класі навчаються на 6 учнів більше, ніж у 6 - Б, у 6 - Б навчаються 30% загальної кількості шестикласників, а кількість учнів у 6 - В класу становить 1/2 кількості учнів 6 - А і 6 - Б класів разом. Скільки учнів у кожному класі? Будь ласка даю 50 балів ЧИТАЙТЕ УВАЖНО ПИТАННЯ задача вирішується через нехай

Answer 1

Ответ:

33 учащихся; 27 учащихся; 30 учащихся

Пошаговое объяснение:

6А на 6 уч. больше. чем в 6Б ?

6Б 30% от общего количества?

6В 1/2 от учащ. 6А и 6Б ?

30%=0.3;

пусть в трех шестых классах учится х человек, тогда в 6Б   0.3х учащихся, в 6А   0.3х+6 человек, в 6В 0.5*((0.3х+0.3х+6)=

0.3х+3,

составим и решим уравнение

0.3х+3+0.3х+0.3х+6+0.3х=х

х-0.9х=9

0.1х=9

х=90

В трех классах 90 человек,

В  6Б 0.3*90=27/учащихся/

в 6А 27+6=33/учащихся/,

в 6В 27+3=30 /учащихся/

Answer 2

Problem Analysis

We are given that there are three sixth-grade classes in a school: 6-A, 6-B, and 6-C. We need to determine the number of students in each class based on the given information.

Let's break down the information provided: - The number of students in class 6-A is 6 more than the number of students in class 6-B. - The number of students in class 6-B is 30% of the total number of sixth-grade students. - The number of students in class 6-C is half the total number of students in classes 6-A and 6-B combined.

Solution

Let's assume the total number of students in classes 6-A and 6-B combined is x.

According to the given information, the number of students in class 6-B is 30% of x. This can be expressed as:

Number of students in class 6-B = 0.3x

The number of students in class 6-A is 6 more than the number of students in class 6-B. This can be expressed as:

Number of students in class 6-A = Number of students in class 6-B + 6

The number of students in class 6-C is half the total number of students in classes 6-A and 6-B combined. This can be expressed as:

Number of students in class 6-C = 0.5(x + Number of students in class 6-A + Number of students in class 6-B)

To solve this system of equations, we can substitute the expressions for the number of students in class 6-B and class 6-A into the equation for class 6-C.

Let's solve the equations step by step:

1. Substitute the expression for the number of students in class 6-B into the equation for class 6-A: Number of students in class 6-A = 0.3x + 6

2. Substitute the expressions for the number of students in class 6-B and class 6-A into the equation for class 6-C: Number of students in class 6-C = 0.5(x + (0.3x + 6) + 0.3x)

3. Simplify the equation for class 6-C: Number of students in class 6-C = 0.5(1.6x + 6)

4. Solve for x by equating the number of students in class 6-C to the given value of 6-B: 0.3x = 0.5(1.6x + 6)

5. Solve for x: x = 20

Now that we have the value of x, we can substitute it back into the equations to find the number of students in each class:

- Number of students in class 6-B = 0.3x = 0.3 * 20 = 6 - Number of students in class 6-A = 0.3x + 6 = 0.3 * 20 + 6 = 12 - Number of students in class 6-C = 0.5(1.6x + 6) = 0.5(1.6 * 20 + 6) = 16

Therefore, there are 6 students in class 6-B, 12 students in class 6-A, and 16 students in class 6-C.

Answer: There are 6 students in class 6-B, 12 students in class 6-A, and 16 students in class 6-C.