Question

Your younger sibling runs up to you and excitedly exclaims, "I'm thinking of a number. If I add it to the number 2 ten times, that is, 2 + my number + my number + my number, and so on, then the answer is 2. What is my number?" You almost immediately answer, "zero," but are you sure? Can you find a different number (other than zero) that has the same property? If not, can you justify that your answer is the only correct answer?

Answer 1

`x = 0`

Explanation:

Given

Represent the number with x.

So:

`2 + x + x + x + x + x + x + x + x + x + x = 2`

or

`2 + 10x = 2`

We want to solve for x

Subtract both sides by 2

`2 - 2 + 10x = 2 - 2`

`10x = 0`

Solve for x

`x = (0)/(10)`

`x = 0`

No other number aside 0, satisfy the property.