4. Тип 3 № 9972 К задуманному числу прибавили шестую часть этого же числа, и получилось 252. Найдите задуманное число.

Let the unknown number be $$x$$. According to the problem, we have: $$x + \frac{1}{6}x = 252$$ Now, we need to solve this equation to find the value of $$x$$. First, we can rewrite the equation as: $$\frac{6}{6}x + \frac{1}{6}x = 252$$ $$\frac{7}{6}x = 252$$ Now, we can multiply both sides of the equation by $$\frac{6}{7}$$ to isolate $$x$$: $$x = 252 \cdot \frac{6}{7}$$ $$x = \frac{252 \cdot 6}{7}$$ Now, divide 252 by 7: $$252 \div 7 = 36$$ So, $$x = 36 \cdot 6$$ $$x = 216$$ Therefore, the unknown number is 216. Answer: 216