Question

Из рулона ткани сшили пододеяльники,простыни и наволочки.На пошив пододеяльников ушло без 6 метров 0,4 рулона.На пошив простыней ушло без 4 метров 0,6 от остатка рулона.Когда без 3 метров 0,75 от нового остатка рулона пошили наволочки,в рулоне осталось 10 м ткани.Сколько метров ткани было в рулоне?Сколько метров ткани ушло на пошив пододеяльников,простыней?

Answer 1

Пусть х метров было в рулоне. 
1)На пошив пододеяльника ушло 0,4 рулона без 6 метров: 0,4х-6 

х-(0,4х-6)=х-0,4х+6=0,6х+6 метров рулона осталось. 

2) На пошив простыни ушло без 4 метров 0,6 от остатка рулона: (0,6х+6)*0,6-4=0,36х+3,6-4=0,36х-0,4  

Новый остаток рулона составил: (0,6х+6)- (0,36х-0,4) =0,6х+6 -0,36х+0,4=0,24х+6,4 

3) На наволочки ушло 0,75 без 3 метров от нового остатка: (0,24х+6,4)*0,75-3=0,18х+4,8-3=0,18х+1,8 

Составим уравнение:   
х - (0,4х-6)-(0,36х-0,4)-( 0,18х+1,8)=10 
х-0,4х+6-0,36х+0,4-0,18х-1,8=10 
0,06х+4,6=10 
0,06х=10-4,6 
0,06х=5,4 
х=5,4:0,06 
х=90 метров ткани в рулоне
Ответ: в рулоне было 90 метров ткани.

Проверим: 90*0,4-6=30 метра (пододеяльник)
                 (90-30)*0,6-4=32  метров (простынь)
                 (90-(30+32)*0,75-3=18 метров (наволочки)
                  90-30-32-18=10 метров (остаток ткани) 

Answer 2

Problem Analysis

We are given the information that from a roll of fabric, pillowcases, sheets, and duvet covers were sewn. We are also given the amounts of fabric used for each item. We need to determine the total amount of fabric in the roll and the amount of fabric used for sewing the duvet covers and sheets.

Solution

Let's break down the information given step by step to solve the problem.

1. From the roll of fabric, 6 meters and 0.4 meters were used for sewing the duvet covers. 2. From the remaining fabric, 4 meters and 0.6 meters were used for sewing the sheets. 3. From the new remaining fabric, 3 meters and 0.75 meters were used for sewing the pillowcases. 4. After all the sewing, there were 10 meters of fabric left in the roll.

To find the total amount of fabric in the roll, we need to add up the amounts used for each item and the amount left in the roll.

Let's calculate the total amount of fabric in the roll:

1. For the duvet covers: 6 meters + 0.4 meters = 6.4 meters. 2. For the sheets: 4 meters + 0.6 meters = 4.6 meters. 3. For the pillowcases: 3 meters + 0.75 meters = 3.75 meters. 4. Amount left in the roll: 10 meters.

To find the initial amount of fabric in the roll, we need to subtract the total amount used and the amount left from the initial total.

Let's calculate the initial amount of fabric in the roll:

Initial total = Total used + Amount left = 6.4 meters + 4.6 meters + 3.75 meters + 10 meters = 24.75 meters.

Therefore, the initial amount of fabric in the roll was 24.75 meters.

To find the amount of fabric used for sewing the duvet covers and sheets, we need to subtract the amount left in the roll from the total used for those items.

Let's calculate the amount of fabric used for sewing the duvet covers and sheets:

Total used for duvet covers and sheets = Total used - Amount left = (6.4 meters + 4.6 meters) - 10 meters = 1 meter.

Therefore, the amount of fabric used for sewing the duvet covers and sheets was 1 meter.

Answer

The initial amount of fabric in the roll was