Seriously I'd hate to talk shit about her but she's kinda been pissing me off and so stubborn about it
So I did part time job as a private English tutor and she's my first customer so at first I lower my pay, let's just say it's like a discount. And it was LOW, like half of the normal price of professional ones, cause it was my first time and I'm not sure how much I should charge.
Then I stopped, cause she moved out and her house is much further that her original, and I'm the one going to her house so obviously I need more pay for my transportation. I can walk to her previous house so it's fine, but after she move out? I can't.
I suggested that she come to my place instead if she wants to keep the same price, but she refused so I quit. Then about two weeks ago she requested another private lesson in her old house just for a few days for her exam. Since it's her old house, I agree. EVEN THEN, I clearly said it's two hours per-session and it actually went for three hours on the first day. Thankfully after that it's two hours per-session. And I didn't ask for an extra payment for that extra hour. (IT'S DUMB, I KNOW!!)

Then, JUST NOW she asked another lesson (this time for math). And this time I CLEARLY STATED that I'm taking an hourly payment. And it's not even that expensive, she can cover an hour with like ¼ of her daily pocket money. And SHE STILL DARE TO ASK FOR A DISCOUNT by sayying "Well, since I'm your first customer…"

AND FUCKING HELL I WILL STAND MY GROUND THIS TIME!
I will raise the price from now on
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I think your first mistake was letting her know she was your first cus she's clearly taking advantage of that info and tryna gasligit you into thinking that you should lower the price, also you mentioned you already asked for a low pay, and she went overboard and didn't keep things professional, I suggest if you aren't currently desperate/in need for cash, to just reject any further classes with her and find someone else.
Yep! You're right, that was my first and biggest mistake
I told her about the new price and insist I can't lower it, but she hadn't reply yet. I'm not in desperate need for cash so I'm not gonna take her, even if later she agree for the price I set. I just don't want to have anything to do with her anymore, it's exhausting.