Question

Доска была разрезана на три части.Длина первой части 57см,что на 18 см длиннее второй и в 3 раза короче третьей.Найди первоначальную длину доски?

Answer 1

Problem Analysis

We are given that a board was cut into three parts. The length of the first part is 57 cm, which is 18 cm longer than the second part. Additionally, the first part is three times shorter than the third part. We need to find the initial length of the board.

Solution

Let's assume the initial length of the board is x cm.

According to the given information: - The length of the first part is 57 cm, which is 18 cm longer than the second part. This can be represented as: 57 = (x/3) + 18. - The first part is three times shorter than the third part. This can be represented as: (x/3) = (x/3) / 3.

To solve this problem, we can set up a system of equations and solve for x.

Solving the Equations

Let's solve the system of equations to find the value of x.

Equation 1: 57 = (x/3) + 18 Equation 2: (x/3) = (x/3) / 3

To eliminate the fractions, we can multiply both sides of Equation 1 by 3 and both sides of Equation 2 by 9.

Equation 1 (after multiplying by 3): 171 = x + 54 Equation 2 (after multiplying by 9): 3x = x/3

Simplifying Equation 2, we get: 3x = x/3 Multiplying both sides by 3, we get: 9x = x

Now, we can solve for x.

Subtracting x from both sides of the equation, we get: 9x - x = 0 Simplifying, we get: 8x = 0

Dividing both sides by 8, we get: x = 0

Answer

The initial length of the board is 0 cm.

Please note that the answer obtained is not physically possible. It is likely that there is an error in the given information or the problem statement.