Question

Двое рабочих изготовили 162 детали. Первый работал 8 дней, а второй-15 дней. Сколько деталей изготовил каждый рабочий, если первый изготовил за 5 дней на 3 детали больше,чем второй за 7 дней? Решите системой уравнений! С объяснениями что откуда взялось!!!

Answer 1

Пусть х - деталей изготавливает в день 1 рабочий, у - деталей изготавливает в день 2 рабочий, тогда получаем систему
8х+15у=162
5х=7у+3

х=20,25-1,875у
5*(20,25-1,875у)=7у+3

х=20,25-1,875у
101,25-9,375у=7у+3

х=20,25-1,875у
у=6 - деталей изготавливает в день 2 рабочий

х=20,25-1,875*6=9- деталей изготавливает в день 1 рабочий
Значит за 8 дней 1 изготовил 8*9=72.
2 изготовил 15*6=90.
Ответ: 72 и 90

Answer 2

Problem Analysis

We are given that two workers produced a total of 162 parts. The first worker worked for 8 days, while the second worker worked for 15 days. We need to determine how many parts each worker produced, given that the first worker produced 3 more parts in 5 days than the second worker produced in 7 days.

Solution

Let's assume that the first worker produced x parts per day, and the second worker produced y parts per day.

From the given information, we can form the following equations:

Equation 1: The total number of parts produced by the first worker in 8 days is equal to 162: 8x = 162

Equation 2: The total number of parts produced by the second worker in 15 days is equal to 162: 15y = 162

Equation 3: The first worker produced 3 more parts in 5 days than the second worker produced in 7 days: 5x = 7y + 3

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.

From Equation 1, we can solve for x: x = 162/8 x = 20.25

Substituting the value of x in Equation 3, we get: 5(20.25) = 7y + 3 101.25 = 7y + 3 7y = 101.25 - 3 7y = 98.25 y = 98.25/7 y = 14.0357 (approx.)

Now, we have the values of x and y. Let's calculate the number of parts produced by each worker.

The first worker produced x parts per day for 8 days: Number of parts produced by the first worker = 8x = 8 * 20.25 = 162

The second worker produced y parts per day for 15 days: Number of parts produced by the second worker = 15y = 15 * 14.0357 = 210.5355 (approx.)

Answer

Based on the given information, the first worker produced 162 parts, and the second worker produced approximately 210 parts.