Question

Рабочий должен был за некоторое время изготовить 360. Первые 5 дней он ежедневно изготавливал запланированное количество деталей, а потом ежедневно изготавливал на 4 детали больше и уже за день до срока изготовил 372 детали. Сколько деталей ежедневно должен был изготовить рабочий по плану? Пожалуйста помогите решить очень надо!!!

Answer 1

Problem Analysis

We are given that a worker had to produce a total of 360 parts within a certain time frame. For the first 5 days, the worker produced the planned quantity of parts each day. After that, the worker increased production by 4 parts per day and completed the task 1 day ahead of schedule, producing a total of 372 parts. We need to determine how many parts the worker was supposed to produce each day according to the original plan.

Solution

Let's break down the problem step by step:

1. Calculate the total number of parts produced during the first 5 days: - The worker produced the planned quantity of parts each day, so the total number of parts produced during the first 5 days is: 5 days * (planned quantity of parts per day) = 5 * X, where X is the planned quantity of parts per day.

2. Calculate the total number of parts produced after the first 5 days: - The worker increased production by 4 parts per day, so the total number of parts produced after the first 5 days is: (total number of days - 5) * (planned quantity of parts per day + 4) = (total number of days - 5) * (X + 4).

3. Set up an equation using the information given in the problem: - The total number of parts produced according to the original plan is 360. - The total number of parts produced after the first 5 days is 372. - We can set up the equation: (5 * X) + ((total number of days - 5) * (X + 4)) = 360 + 372.

4. Solve the equation to find the value of X: - Simplify the equation: 5X + (total number of days - 5)(X + 4) = 732. - Expand the equation: 5X + (total number of days - 5)X + 4(total number of days - 5) = 732. - Combine like terms: 5X + X(total number of days - 5) + 4(total number of days - 5) = 732. - Simplify further: X(5 + total number of days - 5) + 4(total number of days - 5) = 732. - Simplify even further: X(total number of days) + 4(total number of days - 5) = 732. - Divide both sides of the equation by the total number of days: X + 4(total number of days - 5)/total number of days = 732/total number of days. - Simplify: X + 4 - 20/total number of days = 732/total number of days. - Move the constant term to the other side of the equation: X = 732/total number of days - 4 + 20/total number of days.

5. Substitute the value of the total number of days given in the problem (5 + remaining days) into the equation to find the value of X: - X = 732/(5 + remaining days) - 4 + 20/(5 + remaining days).

6. Calculate the value of X to find the planned quantity of parts per day: - Substitute the value of X into the equation: planned quantity of parts per day = X.

Let's calculate the planned quantity of parts per day using the given information.

Calculation

The worker produced a total of 372 parts, completing the task 1 day ahead of schedule. Therefore, the total number of days is 5 + 1 = 6.

Substituting the value of the total number of days into the equation: planned quantity of parts per day = 732/(5 + 1) - 4 + 20/(5 + 1) = 732/6 - 4 + 20/6 = 122 - 4 + 20/6 = 118 + 20/6 = 118 + 10/3 = 118 + 3.33 ≈ 121.33.

Therefore, the worker was supposed to produce approximately 121.33 parts per day according to the original plan.

Please note that since the number of parts produced per day is given as a decimal, it is advisable to round it to the nearest whole number or follow any specific rounding instructions provided in the problem statement.