Question

За 15м ткани двух сортов заплатили 2840р. 1м ткани 1 сорта стоит 200р, а 1м ткани 2 сорта 180р. Сколько метров ткани каждого сорта было куплено?

Answer 1

Пусть х - столько метров первого сорта, а у - второго сорта. Тогда 200х + 180у=2840. Также х+у=15 метров.

Имеем систему уравнений

200х+180у=2840

х+у=15

(Решаем: выразим из второго х через у=15-у. Подставим в первое 200(15-у)+180у=2840. Откуда 3000 - 200у+180у = 2840. -20у = -160. у=8. у+х= 15. х+8=15. х = 7.)

Ответ: первого сорта куплено 7 метров такни, а второго - 8 метров.

Answer 2

Problem Analysis

We are given that 15 meters of fabric of two different types were purchased for a total cost of 2840 rubles. The cost of 1 meter of fabric of the first type is 200 rubles, and the cost of 1 meter of fabric of the second type is 180 rubles. We need to determine how many meters of each type of fabric were purchased.

Solution

Let's assume that x meters of fabric of the first type were purchased, and y meters of fabric of the second type were purchased.

According to the given information, the total cost of the fabric is 2840 rubles. We can set up the following equation to represent this:

200x + 180y = 2840

We also know that the total length of fabric purchased is 15 meters:

x + y = 15

Now we have a system of two equations that we can solve to find the values of x and y.

Solving the System of Equations

We can solve the system of equations using the substitution method or the elimination method. Let's use the elimination method.

Multiplying the second equation by 180, we get:

180x + 180y = 2700

Subtracting this equation from the first equation, we eliminate the y variable:

(200x + 180y) - (180x + 180y) = 2840 - 2700

Simplifying, we get:

20x = 140

Dividing both sides by 20, we find:

x = 7

Substituting this value back into the second equation, we can solve for y:

7 + y = 15

Subtracting 7 from both sides, we find:

y = 8

Answer

Therefore, 7 meters of fabric of the first type and 8 meters of fabric of the second type were purchased.

Note: The answer is based on the given information and the assumption that the cost per meter of fabric remains constant throughout the purchase.