Question

.Бригада робітників повинна була виготовити 384 деталі . Перші 5 днів бригада виконувала щодня встановлену норму , а потім кожень день виготовляла на 3 деталі більше , ніж планувалось , тому вже за 1 день до строку було виготовлено 422 деталі . Скільки деталей щодня повинна була виготовити бригада за планом ?Пожалуйста с полным обьяснением .

Answer 1

пусть план бригады составлял Х деталей в день. Тогда срок выпуска 384 деталей равен  384 / X  дней

Повышенное количество деталей бригада производила  384 / X - 6 дней,

поэтому получаем уравнение

 

5 * Х +  (384 / X - 6) * (X + 3) = 422

           (384 - 6 * X) * ( X + 3)

5 * X + --------------------------- - 422 = 0

                            X

5 * X² + 1152 + 384 * X - 6 * X² - 18 * X - 422 * X

---------------------------------------------------------- = 0

                                 X

1152 - 56 * X - X²

---------------------- = 0

            X

X² + 56 * X - 1152 = 0

X₁ = 16   X₂ = -72

Следовательно, по плану бригада должна была выпускать 16 деталей в день.

Answer 2

Нехай щодня бригада мала виготовляти х деталей, тоді за перші 5 днів вона виготовила 5х деталей. Наступні дні бригада щодня виготовляла (х+3) деталей і виготовляла вона їх 384/х - 6 днів. За цей період бригадою виготовлено (х+3)(384/х - 6) деталей. Знаючи, що всього виготовлено 422 деталі, складаємо рівняння:

5х + (х+3)(384/х - 6) = 422

5х + (384(х+3)) - 6х - 18 = 422

5х²+384х+1152-6х²-18х-422х=0

х²+56х-1152=0

Д=3136+4608=7744

х₁=-72 - не підходить

х₂=16

Відповідь. 16 деталей.

 

Answer 3

To solve this problem, let's break it down step by step.

Step 1: Calculate the number of days the brigade worked at the established norm

The brigade worked for the first 5 days at the established norm. We know that during this period, they produced a total of 384 parts.

Step 2: Calculate the excess parts produced after the first 5 days

Starting from the 6th day, the brigade produced 3 more parts each day than planned. By the end of the 6th day, they had already produced a total of 422 parts, which is 38 parts more than the initial plan.

Step 3: Calculate the number of days it took to produce the excess parts

To find out how many days it took to produce the excess parts, we can divide the excess parts (38) by the additional parts produced each day (3). This will give us the number of days it took to produce the excess parts.

38 excess parts / 3 additional parts per day = 12.67 days

Since we can't have a fraction of a day, we round up to the nearest whole number. Therefore, it took the brigade 13 days to produce the excess parts.

Step 4: Calculate the number of parts produced each day according to the plan

To find out how many parts the brigade was supposed to produce each day according to the plan, we need to subtract the excess parts from the total parts produced during the established norm period.

Total parts produced during the established norm period: 384 parts Excess parts: 38 parts

384 parts - 38 parts = 346 parts

Therefore, according to the plan, the brigade was supposed to produce 346 parts each day.

In summary, the brigade was supposed to produce 346 parts each day according to the plan.

Please let me know if you have any further questions!