Question

Учительница написала на доске числа и сказала шестиклассникам выполнить с ним следующие действия: умножить на 2, к результату прибавить 3, потом результат снова умножить на 2, и снова прибавить 3. Вася всё прослушал, и вместо этого умножил число на доске на 3, к результату прибавил 2, потом результат снова умножил на 3, и снова прибавил 2. Как ни странно, у него получился такой же ответ. Какое число могла написать учительница? Укажите все варианты.

Answer 1

Ответ в этом задании будет - 0.2

Answer 2

Problem Analysis

The teacher wrote numbers on the board and instructed the students to perform a series of operations: multiply by 2, add 3, multiply by 2 again, and add 3 again. However, Vasya mistakenly multiplied the number on the board by 3, added 2, multiplied by 3 again, and added 2 again. Surprisingly, he obtained the same result as the teacher. We need to determine what number the teacher could have written on the board.

Solution

Let's assume the number written on the board by the teacher is represented by the variable 'x'. According to the teacher's instructions, the operations performed by the students can be represented as follows:

1. Teacher's instructions: 2x + 3 2. Vasya's operations: 3x + 2

Since Vasya obtained the same result as the teacher, we can set up the following equation:

2x + 3 = 3x + 2

Now, let's solve this equation to find the possible values of 'x'.

Subtracting 2x from both sides of the equation:

3 = x + 2

Subtracting 2 from both sides of the equation:

1 = x

Therefore, the number that the teacher could have written on the board is 1.

Answer

The number that the teacher could have written on the board is 1.