Question

Ателье закупило ткань трех видов. Шелк составляет 1/3 всей ткани, сукно - 90% количества шелка, а остальная ткань - ситец. Какую часть всей ткани составляет ситец? Сколько всего метров ткани было куплено, если ситца купили 165м?

Answer 1

$1- \frac{1}{3} - \frac{1}{3} \cdot0.9=1- \frac{10}{30} - \frac{9}{30} = \frac{11}{30} \\\ 165: \frac{11}{30} =165\cdot \frac{30}{11}=450(m)$
Ответ: 11/30, 450м

Answer 2

Calculation of the Proportion of Calico in the Total Fabric

To determine the proportion of calico in the total fabric, we need to first understand the composition of the fabric. According to the information provided, the atelier purchased three types of fabric: silk, cloth, and calico.

It is stated that silk makes up 1/3 of the total fabric, and cloth accounts for 90% of the quantity of silk. Therefore, we can calculate the proportion of cloth in the total fabric as follows:

1. Calculate the quantity of cloth: 90% of the quantity of silk. 2. Calculate the quantity of calico: The remaining fabric after subtracting the quantity of silk and cloth from the total fabric.

Let's perform the calculations step by step.

1. Calculation of the Quantity of Cloth: - Silk accounts for 1/3 of the total fabric. - Cloth accounts for 90% of the quantity of silk.

To find the quantity of cloth, we can multiply the quantity of silk by 90%:

Quantity of cloth = (1/3) * 0.9 * Total fabric

2. Calculation of the Quantity of Calico: - Calico is the remaining fabric after subtracting the quantity of silk and cloth from the total fabric.

To find the quantity of calico, we can subtract the quantities of silk and cloth from the total fabric:

Quantity of calico = Total fabric - Quantity of silk - Quantity of cloth

Let's proceed with the calculations.

Calculation:

Given that the quantity of calico purchased is 165 meters, we can use this information to find the total quantity of fabric.

Let's assume the total fabric purchased is represented by the variable "x."

1. Calculation of the Quantity of Cloth: - Silk accounts for 1/3 of the total fabric. - Cloth accounts for 90% of the quantity of silk.

The quantity of cloth can be calculated as follows:

Quantity of cloth = (1/3) * 0.9 * x

2. Calculation of the Quantity of Calico: - Calico is the remaining fabric after subtracting the quantity of silk and cloth from the total fabric.

The quantity of calico can be calculated as follows:

Quantity of calico = x - (1/3) * x - (1/3) * 0.9 * x

Given that the quantity of calico is 165 meters, we can set up the equation:

165 = x - (1/3) * x - (1/3) * 0.9 * x

Now, let's solve the equation to find the value of x, which represents the total quantity of fabric.

Solution:

To solve the equation, we can simplify the expression on the right side:

165 = x - (1/3) * x - (1/3) * 0.9 * x

Simplifying further:

165 = x - (1/3) * x - (3/10) * x

Combining like terms:

165 = (10/10) * x - (3/10) * x - (3/10) * 0.9 * x

Simplifying the expression on the right side:

165 = (7/10) * x - (3/10) * 0.9 * x

Calculating the value of (3/10) * 0.9:

165 = (7/10) * x - (27/100) * x

Combining like terms:

165 = (70/100) * x - (27/100) * x

Simplifying the expression:

165 = (43/100) * x

To isolate x, we can multiply both sides of the equation by (100/43):

(100/43) * 165 = x

Calculating the value:

Approximately x = 383.72

Therefore, the total quantity of fabric purchased is approximately 383.72 meters.

Now, let's calculate the proportion of calico in the total fabric.

Calculation of the Proportion of Calico:

To find the proportion of calico in the total fabric, we can substitute the value of x into the equation for the quantity of calico:

Quantity of calico = x - (1/3) * x - (1/3) * 0.9 * x

Substituting the value of x:

Quantity of calico = 383.72 - (1/3) * 383.72 - (1/3) * 0.9 * 383.72

Simplifying the expression:

Quantity of calico = 383.72 - (1/3) * 383.72 - (3/10) * 383.72

Calculating the value of (1/3) * 383.72:

Quantity of calico = 383.72 - (1/3) * 383.72 - (3/10) * 383.72

Simplifying further:

Quantity of calico = 383.72 - (127.9067) - (115.116)

Calculating the value:

Quantity of calico ≈ 140.6933

Therefore, the quantity of calico in the total fabric is approximately 140.6933 meters.

To summarize: - The proportion of calico in the total fabric is approximately 140.6933 meters out of 383.72 meters. - The total quantity of fabric purchased is approximately 383.72 meters.

Please note that the calculations provided are based on the information given in the question and may be subject to rounding errors.