In my algebraic version, it’s x.

Maybe easier to understand is if we use the numbers from the story?
As the top level comment sees it (which again is the most logical way to interpret it), the price starts at $20. Seller gives 50% discount to buyer to bring it to $10 (50% of $20 is $10 -> $20-$10=$10). Seller then adds a 50% markup because it’s their birthday too, bringing it up to $15 (50% of $10 is $5 -> $10+$5=$15).

In my interpretation all of the math is being operated on the initial $20. So it’s $20 minus $10 for $10 for the discount, then $10 plus $10 for the markup.