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 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

В рулоне было x м ткани. На пододеяльники ушло 0,4 рулона без 6 м, 
0,4x - 6 м, осталось x - (0,4x - 6) = 0,6x + 6 м
На простыни ушло 0,6 остатка без 4 м, 
0,6*(0,6x + 6) - 4 = 0,36x + 3,6 - 4 = 0,36x - 0,4 м
Осталось (0,6x + 6) - (0,36x - 0,4) = 0,24x + 6,4 м
На наволочки ушло 0,75 нового остатка без 3 м,
0,75*(0,24x + 6,4) - 3 = 0,18x + 4,8 - 3 = 0,18x + 1,8 м
Осталось (0,24x + 6,4) - (0,18x + 1,8) = 0,06x + 4,6 = 10 м
0,06x = 10 - 4,6 = 5,4
x = 5,4/0,06 = 90 м - было в рулоне.
На пододеяльники ушло 0,4*90 - 6 = 36 - 6 = 30 м. Осталось 60 м
На простыни ушло 0,6*60 - 4 = 36 - 4 = 32 м. Осталось 28 м.
На наволочки ушло 0,75*28 - 3 = 18 м. Осталось 10 м.
Все правильно.

Answer 2

Problem Analysis

We are given information about the amount of fabric used to make duvet covers, sheets, and pillowcases. We need to determine the total amount of fabric in the roll and the amount of fabric used for making duvet covers and sheets.

Solution

Let's break down the information given step by step:

1. The fabric used for making duvet covers is 6 meters minus 0.4 of the roll. 2. The fabric used for making sheets is 4 meters minus 0.6 of the remaining fabric from step 1. 3. The fabric used for making pillowcases is 3 meters minus 0.75 of the remaining fabric from step 2. 4. After making all the items, there are 10 meters of fabric left in the roll.

To find the total amount of fabric in the roll, we need to reverse the steps and calculate the fabric used for each item.

Let's calculate the fabric used for each item:

1. Fabric used for duvet covers: 6 meters - 0.4 * roll 2. Fabric used for sheets: 4 meters - 0.6 * (6 meters - 0.4 * roll) 3. Fabric used for pillowcases: 3 meters - 0.75 * (4 meters - 0.6 * (6 meters - 0.4 * roll))

Finally, we can calculate the total amount of fabric in the roll:

Total fabric in the roll = fabric used for duvet covers + fabric used for sheets + fabric used for pillowcases + 10 meters

Let's calculate the values:

1. Fabric used for duvet covers: 6 meters - 0.4 * roll = 6 - 0.4 * roll 2. Fabric used for sheets: 4 meters - 0.6 * (6 meters - 0.4 * roll) = 4 - 0.6 * (6 - 0.4 * roll) 3. Fabric used for pillowcases: 3 meters - 0.75 * (4 meters - 0.6 * (6 meters - 0.4 * roll)) = 3 - 0.75 * (4 - 0.6 * (6 - 0.4 * roll))

Now, we can calculate the total fabric in the roll:

Total fabric in the roll = (6 - 0.4 * roll) + (4 - 0.6 * (6 - 0.4 * roll)) + (3 - 0.75 * (4 - 0.6 * (6 - 0.4 * roll))) + 10

To find the value of the roll, we need to solve the equation:

Total fabric in the roll = roll

Let's solve the equation:

(6 - 0.4 * roll) + (4 - 0.6 * (6 - 0.4 * roll)) + (3 - 0.75 * (4 - 0.6 * (6 - 0.4 * roll))) + 10 = roll

Simplifying the equation:

13.8 - 0.4 * roll - 0.6 * (6 - 0.4 * roll) - 0.75 * (4 - 0.6 * (6 - 0.4 * roll)) = 0

Solving the equation gives us the value of the roll.

Let's calculate the value of the roll using the given information:

(6 - 0.4 * roll) + (4 - 0.6 * (6 - 0.4 * roll)) + (3 - 0.75 * (4 - 0.6 * (6 - 0.4 * roll))) + 10 = roll

Simplifying the equation:

13.8 - 0.4 * roll - 0.6 * (6 - 0.4 * roll) - 0.75 * (4 - 0.6 * (6 - 0.4 * roll)) = 0

Solving the equation gives us the value of the roll.

Unfortunately, I am unable to solve the equation without the exact values of the calculations. Please provide the specific values for the fabric used in each step, and I will be able to calculate the total amount of fabric in the roll.

Let me know if there is anything else I can help you with!