Question

один рабочий в день выпускал на 50 деталей меньше другого. Когда выработка первого повысилась на 1% в день, а второго -на 2%, они стали вместе выпускать в день 254 детали. Сколько деталей в день выпускал первоначально каждый рабочий?

Answer 1

Первый выпускал х
второй х+50

выработка первого повысилась на 1% стала 1,01*(х)
выработка второго стала 1,02(х+50)

1,01х+1,02(х+50)=254
1,01х+1,02х+51=254
2,03х=203
х=100 деталей первый
х+50=150 второй

Answer 2

Problem Analysis

We are given that one worker produces 50 fewer parts per day than another worker. When the production of the first worker increases by 1% per day and the production of the second worker increases by 2% per day, they together produce 254 parts per day. We need to determine how many parts each worker initially produced per day.

Solution

Let's assume that the initial production of the first worker is x parts per day. Since the second worker produces 50 fewer parts per day, their initial production would be x - 50 parts per day.

When the production of the first worker increases by 1% per day, their new production becomes x + 0.01x = 1.01x parts per day. Similarly, when the production of the second worker increases by 2% per day, their new production becomes (x - 50) + 0.02(x - 50) = 1.02(x - 50) parts per day.

According to the given information, the total production when they work together is 254 parts per day. Therefore, we can set up the following equation:

1.01x + 1.02(x - 50) = 254

Simplifying the equation:

1.01x + 1.02x - 51 = 254

2.03x = 305

x = 150

Therefore, the initial production of the first worker was 150 parts per day.

To find the initial production of the second worker, we substitute the value of x into the equation:

x - 50 = 150 - 50 = 100

Therefore, the initial production of the second worker was 100 parts per day.

Answer

The first worker initially produced 150 parts per day, while the second worker initially produced 100 parts per day.