Question

В двух кусках поровну ткани. После того как от первого куска продали 14 метров, а от второго 22 метра, в первом куске осталось втрое больше ткани, чем во втором. Сколько метров ткани было в каждом куске первоначально? (Решить уровниием)

Answer 1

Осталось во втором куске х
осталось в первом куске 3х
было в первом куске 3х+14
было во втором куске х+22
составим уравнение
3х+14=х+22
3х-х=22-14
2х=8
х=8:2
х=4 м осталось во втором куске
4+22=26 м было во втором куске
3*4=12 м осталось в первом куске
12+14=26 м было в первом куске
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Answer 2

Solving the Equation for the Amount of Fabric in Each Piece Initially

To solve this problem, we can use a system of equations. Let's denote the initial amount of fabric in the first piece as x and in the second piece as y.

We are given the following information: 1. After selling 14 meters from the first piece and 22 meters from the second piece, there was three times more fabric left in the first piece than in the second piece. 2. The total amount of fabric sold from both pieces is equal to the difference between the initial amounts of fabric in the two pieces.

Using this information, we can set up the following system of equations: 1. x - 14 = 3(y - 22) (equation representing the first piece after selling 14 meters and the second piece after selling 22 meters) 2. 14 + 22 = x - y (equation representing the total amount of fabric sold from both pieces)

Let's solve this system of equations to find the initial amounts of fabric in each piece.

Solving the System of Equations

We can solve the system of equations using the substitution method. First, we'll solve equation (1) for x and then substitute it into equation (2).

1. From equation (1): x = 3(y - 22) + 14 2. Substitute x into equation (2): 3(y - 22) + 14 - y = 36 3. Simplify the equation: 3y - 66 + 14 - y = 36 4. Combine like terms: 2y - 52 = 36 5. Add 52 to both sides: 2y = 88 6. Divide by 2: y = 44 7. Substitute y back into equation (1) to find x: x = 3(44 - 22) + 14 = 3(22) + 14 = 66 + 14 = 80

Answer

So, the initial amount of fabric in the first piece was 80 meters and in the second piece was 44 meters.