Question

Сева задумал натуральное число. Он умножил это число на 3, затем прибавил задуманное число, а к результату прибавил 17. В итоге у него получилось число 752. Докажите, что Сева ошибся в подсчетах.

Answer 1

НАпример задуманное число будет Х. Если Х умножить на 3 получиться 3Х. Потом 3Х+Х= 4Х. Затем 4Х+17=752
4Х=752-17
4Х=735
Х=765:4
Мы не сможем разделить 765 на 4 без остатка.
Значит Сева ошибся в подсчётах

Answer 2

Problem Analysis

Seva has made some calculations and arrived at a result of 752. However, we need to prove that Seva made a mistake in his calculations. To do this, we will analyze the given information and perform the calculations step by step.

Given Information

- Seva thought of a natural number. - He multiplied this number by 3. - He then added the original number to the result. - Finally, he added 17 to the previous result, resulting in 752.

Solution

Let's assume the original number Seva thought of is x.

According to the given information, Seva multiplied the original number by 3, which gives us 3x. He then added the original number to this result, resulting in 3x + x = 4x. Finally, he added 17 to this result, giving us 4x + 17.

We are given that the final result is 752. Therefore, we can set up the following equation:

4x + 17 = 752

To solve for x, we need to isolate it on one side of the equation. Let's solve the equation step by step:

4x + 17 = 752

Subtract 17 from both sides:

4x = 752 - 17

Simplify:

4x = 735

Now, divide both sides by 4 to solve for x:

x = 735 / 4

Performing the division:

x = 183.75

Since Seva was thinking of a natural number, the result should be a whole number. However, 183.75 is not a whole number, which means Seva made a mistake in his calculations.

Therefore, we have proven that Seva made an error in his calculations.

Conclusion

Seva made a mistake in his calculations. The original number he thought of cannot be a decimal like 183.75, as he was looking for a natural number.