Question

Алеша задумал число. Он ррибавил к нему 5, потом разделил сумму на 3, умножил на 4, отнял 6, разделил на 7 и получил число 2. Какое число он задумал

Answer 1

Alesh's Number Puzzle

Alesh started with an unknown number and performed a series of mathematical operations on it. Let's break down the steps and find out the number he had in mind.

1. Alesh added 5 to the number. 2. He then divided the sum by 3. 3. Next, he multiplied the result by 4. 4. After that, he subtracted 6 from the product. 5. Finally, he divided the difference by 7 and obtained the number 2.

To find the original number, we can work backward through the steps.

Let's denote the unknown number as x.

Step 1: Alesh added 5 to the number. The result of this step is x + 5.

Step 2: He divided the sum by 3. The result of this step is (x + 5) / 3.

Step 3: Alesh multiplied the result by 4. The result of this step is 4 * ((x + 5) / 3).

Step 4: He subtracted 6 from the product. The result of this step is 4 * ((x + 5) / 3) - 6.

Step 5: Finally, he divided the difference by 7 and obtained the number 2. The equation for this step is (4 * ((x + 5) / 3) - 6) / 7 = 2.

To find the value of x, we can solve this equation:

(4 * ((x + 5) / 3) - 6) / 7 = 2

Simplifying the equation:

(4 * (x + 5) - 18) / 21 = 2

Multiplying both sides of the equation by 21 to eliminate the denominator:

4 * (x + 5) - 18 = 42

Expanding the equation:

4x + 20 - 18 = 42

Simplifying further:

4x + 2 = 42

Subtracting 2 from both sides:

4x = 40

Dividing both sides by 4:

x = 10

Therefore, the number Alesh had in mind is 10.