Question - Finding a Specific Number

Let the three-digit number be represented as \(x\).

When we append the digit 2 to the right of \(x\), we get the new number \(10x + 2\).

According to the problem, this new number is 106 more than the original number:

$$10x + 2 = x + 106$$

Simplifying gives:

$$10x + 2 - x = 106$$

$$9x + 2 = 106$$

Subtracting 2 from both sides:

$$9x = 104$$

Dividing both sides by 9 gives:

$$x = \frac{104}{9} \approx 11.56$$

Since \(x\) must be a three-digit integer, we reevaluate earlier calculations and constraints.