Technically he would have to charge $15… If he would add 50% to the initial $20.
Yes, I’m a lot of fun at parties
You could make it work mathematically: the added 50% would need to be based on the initial price and not a modification on the adjusted price.
It’s most logically interpreted as: x * 1.5 * 0.5 = 0.75x
But we could see it as: x - (x/2) + (x/2) = x
I’m equally fun at parties.
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.