Prealgebra-number theory

Question

Given a positive integer $N$. Deleting the last digit of $N$ will decrease it by $2011$. What is $N$?

I know the answer, but can anyone show the working?

Answer 1

Let $N = \overline{Ax}$. One then has $$\overline{Ax} - A = 2011.$$ $$9A + x = 2011.$$

So, $2011-x = 9A$. Try $x$ from 0 to 9, you will get $A = 223$, $x=4$.

Answer 2

Hint:

Let $N=10x+a$ for some $0\le a\le 9$

Answer 3

X + 2011 = 10X + e where e is a one digit error X = 2011/9 - e and e is still an error, not sure if is the same as the other e X = 223 + another e I am ignoring So 223e - 223 = 2011, and this e I will solve. It is 4. The answer is 2234. Simple, more puzzle than math, and it can be solved with 7th grade notation.