Question

Токарь и его ученик вместе за смену выточили 130 деталей. Сколько деталей выточил каждый из них, если часть деталей, которую выточил токарь, уменьшенная в 3 раза, была равна деталям, которые выточил ученик, увеличенным в 4 раза?

Answer 1

Система Х:3=у*4. Х+у=130 Из первого выражаем х. Х=у*4*3=12у и подставляем во второе 12у+у=130 13у=130 У=10 деталей сделал ученик 130-10=120 деталей сделал учитель

Answer 2

Problem Analysis

We are given that a turner (tokar) and his apprentice (uchenik) together produced 130 parts during a shift. We need to determine how many parts each of them produced, given that the number of parts produced by the turner is three times smaller than the number of parts produced by the apprentice, and the number of parts produced by the apprentice is four times larger than the original number.

Solution

Let's assume that the number of parts produced by the apprentice is x. According to the given information, the number of parts produced by the turner is three times smaller than x, which is x/3. The number of parts produced by the apprentice is four times larger than the original number, which is 4x.

We can set up the following equation to represent the total number of parts produced:

x + x/3 = 130

To solve this equation, we can multiply through by 3 to eliminate the fraction:

3x + x = 390

Simplifying the equation, we have:

4x = 390

Now, we can solve for x by dividing both sides of the equation by 4:

x = 390/4 = 97.5

Since we cannot have a fraction of a part, we need to round the value of x to the nearest whole number. Therefore, the apprentice produced approximately 98 parts.

To find the number of parts produced by the turner, we can substitute the value of x into the equation x/3:

98/3 ≈ 32.67

Again, we need to round this value to the nearest whole number. Therefore, the turner produced approximately 33 parts.

Answer

The apprentice produced approximately 98 parts, while the turner produced approximately 33 parts.