Question

За 15 метров ткани двух сортов заплатили 2840 рублей. При этом 1 метр ткани I сорта стоит 200 рублей,а II сорта -180 рублей. Сколько метров ткани каждого сорта куплено?

Answer 1

X - 1 сорт ткани
y - 2 сорт ткани
составляем систему
x+y=15
200x+180y=2840

находим y из первого уравнения
y=15-x
подставляем y во второе уравнение и решаем его
200x+180(15-x)=2840
200x+2700-180x=2840
20x=2840-2700
x=140/20
x=7
подставляем x в первое уравнение и находим y
7+y=15
y=15-7
y=8
Ответ: Купили 7 метров ткани 1 сорта и 8 метров ткани 2 сорта

Answer 2

Calculating the Amount of Fabric Bought

To solve this problem, we can use a system of linear equations. Let's denote the number of meters of fabric of the first and second sorts as x and y respectively. We have the following information:

1. The total cost for 15 meters of fabric is 2840 rubles. 2. The cost of 1 meter of fabric of the first sort is 200 rubles, and the cost of 1 meter of fabric of the second sort is 180 rubles.

We can express this information in the form of equations and solve for x and y.

Formulating the Equations

The total cost equation can be expressed as: 200x + 180y = 2840 (equation 1)

The total amount of fabric equation can be expressed as: x + y = 15 (equation 2)

Solving the Equations

We can solve this system of equations to find the values of x and y.

Solution

Using the substitution method, we can solve equation 2 for x: x = 15 - y

Substitute the value of x in equation 1: 200(15 - y) + 180y = 2840 3000 - 200y + 180y = 2840 20y = 2840 - 3000 20y = -160 y = -160 / 20 y = -8

Substitute the value of y in equation 2: x + (-8) = 15 x = 15 + 8 x = 23

Answer

The solution to the system of equations is: x = 23 meters of fabric of the first sort y = 8 meters of fabric of the second sort