Question

чтобы связать свитер, шапочку и шарф взяли 1 кг 200 г шерсти. На шарф потребовалось на 100 г шерсти больше, чем на шапочку, и на 400 г меньше чем на свитер. Сколько граммов шерсти израсходовали на каждую вещь?

Answer 1

х - кол-во шерсти на шарф

х-100 - кол-во шерсти на шапку

х+400 - кол-во шерсти на свитер

х+х-100+х+400=1200

3х=1200+100-400

3х=900

х=300 (г) - на шарф

300-100=200 (г ) на шапку

300+400=700 (г) - на свитер

Answer 2

свитер- x

шапочка- z

шарф- q

 

x+z+q=1200

q-100=z

q+400=x

 

решаем систему

из 2 вычтем 3 уравнение

-500=z-x

z=-500+x

q=x-400

вставляем в первое уравнение

x-500+x+x-400=1200

3x=2100

x=700

z=200

q=300

 

Answer 3

Calculation of Wool Usage for Sweater, Hat, and Scarf

To calculate the amount of wool used for each item (sweater, hat, and scarf), we are given that a total of 1 kg 200 g of wool was used. Additionally, we know that the scarf required 100 g more wool than the hat and 400 g less wool than the sweater.

Let's break down the calculation step by step:

1. Total amount of wool used: 1 kg 200 g = 1200 g.

2. Let's assume the amount of wool used for the hat is x g.

3. The scarf required 100 g more wool than the hat, so the amount of wool used for the scarf is (x + 100) g.

4. The scarf required 400 g less wool than the sweater, so the amount of wool used for the sweater is (x + 100 + 400) g = (x + 500) g.

5. The total amount of wool used for all three items is the sum of the wool used for each item: x g + (x + 100) g + (x + 500) g = 1200 g.

Now, let's solve the equation to find the value of x, which represents the amount of wool used for the hat:

x + (x + 100) + (x + 500) = 1200

3x + 600 = 1200

3x = 600

x = 200

Therefore, the amount of wool used for the hat is 200 g.

Using this information, we can calculate the amount of wool used for each item:

- Hat: 200 g (as calculated above). - Scarf: 200 g + 100 g = 300 g. - Sweater: 200 g + 500 g = 700 g.

So, the amount of wool used for each item is as follows: - Hat: 200 g. - Scarf: 300 g. - Sweater: 700 g.

Please note that these calculations are based on the given information and assumptions made.