Question

Гриша задумал натуральное число,умножил его на 9 ,затем отнял задуманное число, из этого результата отнял 21 и у него получилось 752. Докажите,что он ошибся в расчете.

Answer 1

Обзовём число Гриши x
Тогда по условию (752+21+x)/9=x
Посчитаем:
По правилу пропорции 752+21+x=9x
773+x=9x
773=8x
x=96,625
96,625 не натуральное число следовательно Гриша ошибся в расчётах. ч.т.д.

Answer 2

Problem Analysis

Grisha has performed a series of calculations with a natural number, and he claims that the final result is 752. We need to verify whether Grisha made a mistake in his calculations.

Calculation Steps

Grisha's calculations can be broken down into the following steps: 1. He multiplied a natural number by 9. 2. He subtracted the original number from the result of the multiplication. 3. He subtracted 21 from the previous result. 4. The final result obtained by Grisha is 752.

Let's Solve the Problem

To prove that Grisha made a mistake in his calculations, we need to reverse the steps and find the original number.

Let's assume the original number is x.

1. Grisha multiplied the original number by 9, so the result is 9x. 2. Grisha subtracted the original number from the result of the multiplication, so the result is 9x - x = 8x. 3. Grisha subtracted 21 from the previous result, so the result is 8x - 21. 4. The final result obtained by Grisha is 752, so we have the equation 8x - 21 = 752.

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

8x - 21 = 752

Adding 21 to both sides of the equation:

8x = 752 + 21 8x = 773

Dividing both sides of the equation by 8:

x = 773 / 8 x = 96.625

Since x is a natural number, we can conclude that Grisha made a mistake in his calculations. The original number cannot be a decimal value like 96.625.

Therefore, Grisha's claim that the final result is 752 is incorrect.

Conclusion

Grisha made a mistake in his calculations. The original number cannot be a decimal value, so his claim that the final result is 752 is incorrect.