An algebra problem by swastik p (6)

Algebra Level pending

The sum of the digits of a number $10^n-7$ is $3792$ then what is the value of $'n'$ ?

1 solution

S P
May 26, 2018

$10^n-7= \underbrace{99\cdots 999}_{n-1~~~ \text{nines}}3$

$\therefore \begin{aligned} 3792 & =\underbrace{9+9+\cdots +9+9+9}_{n-1~~~ \text{nines}}+3\\& =9(n-1)+3\\& =9n-6\end{aligned}$

Hence, $3792+6=3798=9n \implies 3798/9=\boxed{422}=n$