Question

Майстер має зробити 120 деталей якщо він буде виготовляти щодна на 2 деталі більше ніж повинен то закінчить роботу на 2 дні раніше. Скільки деталей за день має виготовляти майстер? ​

Answer 1

Пусть х деталей в день - план, тогда (х + 2) деталей в день - факт. Уравнение:

120/х - 120/(х+2) = 2

120 · (х + 2) - 120 · х = 2 · х · (х + 2)

120х + 240 - 120х = 2х² + 4х

2х² + 4х - 240 = 0

Разделим обе части уравнения на 2

х² + 2х - 120 = 0

D = b² - 4ac = 2² - 4 · 1 · (-120) = 4 + 480 = 484

√D = √484 = 22

х₁ = (-2-22)/(2·1) = (-24)/2 = -12 (не подходит, так как < 0)

х₂ = (-2+22)/(2·1) = 20/2 = 10

Вiдповiдь: 10 деталей за день має виготовляти майстер.

Answer 2

Calculation of Daily Production

To find out how many parts the master should produce per day, we can set up an equation based on the given information.

Let's assume that the master should produce x parts per day. According to the problem, if the master produces 2 more parts per day than required, he will finish the work 2 days earlier. Therefore, we can set up the following equation:

(x + 2) * (number of days - 2) = 120

Simplifying the equation, we get:

x * (number of days - 2) = 120 - 2 * (number of days - 2)

Now, let's solve this equation to find the value of x, which represents the number of parts the master should produce per day.

Please note that we don't have enough information about the number of days given in the problem. If you can provide the number of days, we can calculate the daily production accordingly.