A 100% increase followed by a 50% decrease

We end up with our original number!

We end up with our original number

Step-by-step explanation:

Let x be our number

We increase by 100

increase = old number * 100%

increase = x*1

increase = x

New number = old number + increase

= x+x

=2x

Now we decrease by 50%

decrease = number * 50%

= 2x*.5

=x

Final number = new number - decrease

= 2x-x

=x