Question

ПОМОГИТЕ РЕШИТЬ ЗАДАЧУ,ПОЖАЛУЙСТА!Первый рабочий работал 7дней,а второй-9дней.Вместе они изготовили 174детали.Сколько деталей в день изготавливал каждый рабочий,если первый рабочий за 1 день изготавливал на 8деталей меньше чем второй за 2дня?

Answer 1

Х-деталей первый за день
х+8 второй за 2 дня
$\frac{x+8}{2}$ -второй за день

7х+9($\frac{x+8}{2}$)=174
14х+9х+72=348
23х=348-72
23х=276
х=12(дет)-первый за день
$\frac{x+8}{2} = \frac{12+8}{2} =10$ второй рабочий за день

Ответ:12 и 10 деталей.

системой так
х-деталей делал первый за день
у-второй за день

7х+9у=174
2у-х=8  умножим на 7

7х+9у=174
14у-7у=56  сложим
23у=230
у=10(дет)-второй рабочий за день
2*10-х=8
20-х=8
х=12(дет)-второй рабочий за день

Answer 2

Problem Analysis

We are given that the first worker worked for 7 days and the second worker worked for 9 days. Together, they produced a total of 174 items. We need to determine how many items each worker produced per day, given that the first worker produced 8 fewer items per day than the second worker over a span of 2 days.

Solution

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

From the given information, we can form the following equations: 1. The first worker worked for 7 days, so the total number of items produced by the first worker is 7x. 2. The second worker worked for 9 days, so the total number of items produced by the second worker is 9y. 3. Together, they produced a total of 174 items, so we have the equation 7x + 9y = 174. 4. The first worker produced 8 fewer items per day than the second worker over a span of 2 days, so we have the equation 2(y - x) = 8.

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

Solving the System of Equations

Let's solve the system of equations using the substitution method.

From equation 4, we can rewrite it as y - x = 4.

Solving equation 4 for y, we get y = x + 4.

Substituting this value of y into equation 3, we have 7x + 9(x + 4) = 174.

Simplifying the equation, we get 7x + 9x + 36 = 174.

Combining like terms, we have 16x + 36 = 174.

Subtracting 36 from both sides, we get 16x = 138.

Dividing both sides by 16, we get x = 8.625.

Substituting this value of x into equation 4, we have y - 8.625 = 4.

Adding 8.625 to both sides, we get y = 12.625.

Answer

Therefore, the first worker produced approximately 8.625 items per day, and the second worker produced approximately 12.625 items per day.

Please note that these values are approximate due to rounding.

Let me know if you need any further assistance!