Question

В одном ателье должны были сшить 180 костюмов, а в другом – 161 костюм. Первое ателье затратило на всю работу на 3 дня меньше, чем второе, так как изготавливало в день на 2 костюма больше. Сколько костюмов в день изготавливало каждое ателье?

Answer 1

Calculation of Daily Production in Each Studio

To determine the number of costumes produced per day in each studio, we can set up a system of equations based on the given information.

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

According to the information provided, the first studio produced a total of 180 costumes, while the second studio produced 161 costumes. Additionally, the first studio took three days less to complete the work compared to the second studio, and it produced two more costumes per day.

Based on these conditions, we can set up the following equations:

Equation 1: x * (y + 2) = 180 (The first studio produced two more costumes per day) Equation 2: y * (x + 3) = 161 (The second studio took three days longer to complete the work)

To solve this system of equations, we can use substitution or elimination methods.

Let's solve it using the substitution method:

From Equation 1, we can express x in terms of y: x = 180 / (y + 2)

Substituting this value of x into Equation 2, we get: (180 / (y + 2)) * (y + 3) = 161

Simplifying the equation: 180(y + 3) = 161(y + 2)

Expanding and simplifying further: 180y + 540 = 161y + 322

Bringing like terms to one side: 180y - 161y = 322 - 540 19y = -218

Dividing both sides by 19: y = -218 / 19 y ≈ -11.47

Since the number of costumes produced cannot be negative, we can disregard this solution.

Therefore, there is no valid solution for the number of costumes produced per day in each studio based on the given information.

Please note that the given information may be incomplete or contradictory, leading to an unsolvable system of equations. If you have any additional information or clarification, I would be happy to assist you further.