Let’s simplify the “riddle”.

It states: a number is 1 plus half that number.

What is a quantity that added to “half a number” gives the number? What do you add to 0,5 to make 1?

The other half.

So we go back to the original statement: “a number is 1 plus half that number” and change it to “a number is half that number plus half that number”.

If you go back and forth between the two you may notice that one the one side there is “1” and on the other “half that number”.

$1 is half the cost, what is the total cost?

We leave the last step to the readers.