Question

первая бригада должна была сшить 160 костюмов, а вторая за тот же срок - на 25 % меньше. первая бригада шила в день на 10 костюмов больше, чем вторая, и выполнила задание за 2 дня до намеченного срока. сколько костюмов в день шила вторая бригада, если ей для выполнения задания понадобилось дополнительно 2 дня?

Answer 1

х кост/день - шила ІІ мастерская

(х+10) кост/день - шила І мастерская

160кост. - 100%

? кост. - 25%

160*0,25=40(кост). - 25%

160-40=120(кост). - должна сшить ІІ мастерская

2+2=4(дня) - на 4дня дольше работала ІІ мастерская,чем І

Уравнение:

120/х - 160/(х+10) = 4, общий знаменатель х(х+10)

120(х+10) -  160х = 4х(х+10)

120х+1200-160х-4х2+40х=0

4х2+80х-1200=0

х2+20х-300=0

х=(-20+40)/2=10(кост). - шила ІІ мастерская

 

Answer 2

Problem Analysis

We are given that the first brigade was supposed to sew 160 costumes, while the second brigade was supposed to sew 25% fewer costumes in the same amount of time. The first brigade sewed 10 costumes more per day than the second brigade and completed the task 2 days ahead of schedule. We need to determine how many costumes per day the second brigade sewed, given that they needed an additional 2 days to complete the task.

Solution

Let's break down the information given: - The first brigade sewed 10 costumes more per day than the second brigade. - The first brigade completed the task 2 days ahead of schedule. - The second brigade needed an additional 2 days to complete the task.

To find the number of costumes sewn per day by the second brigade, we can start by calculating the number of costumes sewn per day by the first brigade.

Let's assume that the second brigade sews x costumes per day. Then, the first brigade sews x + 10 costumes per day.

Since the first brigade completed the task 2 days ahead of schedule, we can set up the following equation:

160 costumes = (x + 10 costumes) * (number of days - 2)

Simplifying the equation:

160 = (x + 10) * (number of days - 2)

Now, we can solve for x, the number of costumes sewn per day by the second brigade.

Calculation

Let's solve the equation to find the number of costumes sewn per day by the second brigade.

160 = (x + 10) * (number of days - 2)

Expanding the equation:

160 = x * (number of days - 2) + 10 * (number of days - 2)

160 = x * number of days - 2x + 10 * number of days - 20

Combining like terms:

160 = (x + 10) * number of days - 2x - 20

Rearranging the equation:

(x + 10) * number of days = 160 + 2x + 20

(x + 10) * number of days = 180 + 2x

Dividing both sides by (x + 10):

number of days = (180 + 2x) / (x + 10)

Since we know that the second brigade needed an additional 2 days to complete the task, we can set up the following equation:

number of days + 2 = (180 + 2x) / (x + 10)

Now, we can solve for x, the number of costumes sewn per day by the second brigade.

Calculation

Let's solve the equation to find the number of costumes sewn per day by