Question

Три цеха за смену изготовили 496 деталей. Второй цех изготовил в 2 раза меньше чем 1, а третий на 56 деталей больше, чем второй. Сколько деталей изготовил каждый цех? Решите с помощью уровнения

Answer 1

2х дет.  -  заготовил 1й цех
х дет.  -  заготовил 2й цех
(х + 56) дет.  -  заготовил 3й
496 дет.  -  всего
? дет.  -  каждый цех

1) 2х + х + (х + 56) = 496
    4х = 496 - 56
    4х = 440
    х = 440 : 4
    х = 110 дет. - заготовил 2й цех
2) 110 * 2 = 220 дет. - заготовил 1й цех
3) 110 + 56 = 166 дет. - 3й цех.

Answer 2

Problem Analysis

We are given information about three workshops that produced a total of 496 parts in one shift. The second workshop produced half as many parts as the first workshop, and the third workshop produced 56 more parts than the second workshop. We need to determine the number of parts produced by each workshop.

Solution

Let's assume the number of parts produced by the first workshop is x. According to the given information, the second workshop produced half as many parts as the first workshop, so the number of parts produced by the second workshop is x/2. The third workshop produced 56 more parts than the second workshop, so the number of parts produced by the third workshop is x/2 + 56.

We know that the total number of parts produced by all three workshops is 496. Therefore, we can write the equation:

x + x/2 + x/2 + 56 = 496

Now, let's solve this equation to find the value of x.

Solving the Equation

To solve the equation, we can combine like terms and simplify:

x + x/2 + x/2 + 56 = 496

Combining like terms:

2x + 56 = 496

Subtracting 56 from both sides:

2x = 496 - 56

2x = 440

Dividing both sides by 2:

x = 440/2

x = 220

Answer

The first workshop produced 220 parts, the second workshop produced 220/2 = 110 parts, and the third workshop produced 110 + 56 = 166 parts.

Therefore, the number of parts produced by each workshop is as follows: - First workshop: 220 parts - Second workshop: 110 parts - Third workshop: 166 parts