Question

Два рабочих за одну смену изготовили 72 детали. После того как, работоспособность первого увеличилась на 15%, а у второго увеличилась на 25% они стали делать за одну смену 86 деталей. Сколько деталей делает каждый рабочий, после увеличения работоспособности? тема сложные проценты,решите пж ​

Answer 1

Ответ:

Пошаговое объяснение:

Пусть работоспособность первого рабочего будет х , второго у  деталей за смену.

х+у=72 (1)

Увеличение работоспособности  первого рабочего

х+0,15х  ;

второго рабочего

у+0,25у.

х+0,15х+у+0,25у=86  (2)

Решаем систему уравнений.

{х+у=72

{1,15х+1,25у=86

Из (1) уравнения.

х=72-у

Подставляем во второе уравнение  и решаем.

0,1у=3,2

у=32 детали до увеличения работоспособности

После

1,25*32=40 деталей  (второй рабочий)

Первый рабочий.

1,15х+40=86

1,15х=46

х=40 деталей.  до увеличения работоспособности.

После

1,15*40=46 деталей.

Answer 2

Problem Analysis

We are given that two workers produced 72 parts in one shift. After their productivity increased by 15% and 25% respectively, they were able to produce 86 parts in one shift. We need to determine how many parts each worker produces after their productivity increases.

Solution

Let's assume that the first worker initially produces x parts in one shift, and the second worker initially produces y parts in one shift.

According to the given information, the total number of parts produced by both workers initially is 72. So we have the equation:

x + y = 72 ---(1)

After the productivity increase, the first worker's productivity increases by 15%, which means their new productivity is 1.15 times their initial productivity. Similarly, the second worker's productivity increases by 25%, which means their new productivity is 1.25 times their initial productivity.

The total number of parts produced by both workers after the productivity increase is 86. So we have the equation:

1.15x + 1.25y = 86 ---(2)

We can solve this system of equations to find the values of x and y.

Solving the System of Equations

To solve the system of equations (1) and (2), we can use the substitution method.

From equation (1), we have:

x = 72 - y

Substituting this value of x into equation (2), we get:

1.15(72 - y) + 1.25y = 86

Simplifying the equation:

82.8 - 1.15y + 1.25y = 86

0.1y = 3.2

y = 32

Substituting the value of y back into equation (1), we get:

x + 32 = 72

x = 40

Answer

After the productivity increase, the first worker produces 40 parts in one shift, and the second worker produces 32 parts in one shift.

Note: The solution provided above is based on the information given in the problem statement.