Question

Рабочие трёх цехов изготовили 869 деталей. Рабочие второго цеха изготовили деталей в 3 раза больше первого, а третьего в 2 раза меньше, чем второго. Сколько деталей изготовили рабочие каждого цеха?

Answer 1

869 * 3 : 2 = 2607 : 2 = 1303,5

Answer 2

Х - изготовил 1-й цех 
3х - второй цех 
3х/2 -  третий цех 
Уравнение 
х + 3х + 3х/2 = 869 
4х + 3х/2 = 869 
11х = 869 * 2 
11х = 1738 
х = 158 дет  изготовил 1-й цех  
158 * 3 = 474 дет  изготовил 2-й цех  
474 : 2 = 237 дет  изготовил 3-й цех  

Проверка 
158 + 474 + 237 = 869 

Answer 3

Problem Analysis

We are given information about the production of parts in three different workshops. The second workshop produces three times as many parts as the first workshop, while the third workshop produces half as many parts as the second workshop. We need to determine the number of parts produced by each workshop.

Solution

Let's assign variables to represent the number of parts produced by each workshop: - Let's call the number of parts produced by the first workshop x. - The second workshop produces three times as many parts as the first workshop, so the number of parts produced by the second workshop is 3x. - The third workshop produces half as many parts as the second workshop, so the number of parts produced by the third workshop is (1/2) * 3x = (3/2)x.

We are given that the total number of parts produced by all three workshops is 869. Therefore, we can write the equation:

x + 3x + (3/2)x = 869

Simplifying the equation:

(2/2)x + (6/2)x + (3/2)x = 869

(11/2)x = 869

To solve for x, we can multiply both sides of the equation by (2/11):

x = (869 * 2) / 11

Now we can calculate the value of x and then find the number of parts produced by each workshop.

Calculation

Let's calculate the value of x:

x = (869 * 2) / 11 = 158

Therefore, the first workshop produced 158 parts.

The second workshop produces three times as many parts as the first workshop:

3x = 3 * 158 = 474

Therefore, the second workshop produced 474 parts.

The third workshop produces half as many parts as the second workshop:

(3/2)x = (3/2) * 158 = 237

Therefore, the third workshop produced 237 parts.

Answer

The number of parts produced by each workshop is as follows: - The first workshop produced 158 parts. - The second workshop produced 474 parts. - The third workshop produced 237 parts.

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