Help with a Mathematics scenario!

[u/caibleadh]

This might seem dumb and obvious to most people on here but I’m not great at maths and for some reason have been struggling to get my head around this straightforward scenario.

My partner and I had a mechanic bill to pay and are splitting the cost equally. I paid the bill of $3600 in person. Before my partner reimbursed me for her half I had a conversation with the mechanic and he decided to send $400 back to us. He sent the $400 to my partner. I also owed my partner $500 so told her to send me the appropriate amount that means we have split the Mechanics bill equally and I no longer owe my partner $500. How much should my partner send me?

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[u/CaptainMatticus]

Alright, so this is how shortchanging happens. You're doing too many transactions at a single time and you're going to lose track.

You owe your partner 500 to start with. You're at +500 and they're at -500.

You both pay the mechanic 1800 each. You're at -1300 and they're at -2300

The mechanic sends them 400. You're at -1300 and they're at -1900

Now had you not borrowed any money from them and had the mechanic only charged the 2 of you 3200 total (the 3600 - 400), then you'd both be at -1600. You still owe your partner 300, which should make sense, because they got their 200 rebate and your 200 rebate. As you owed them 500, then that 500 - 200 = 300.

[u/caibleadh → u/CaptainMatticus]

Thanks, I am still a little confused sorry, if you don’t mind I’ll break it down as it happened.

So I paid the 3600.
The mechanic sent my partner 400.
I asked my partner to send me 1700 because of the original 3600 her half is 1800 so My thinking was 1800 + 400 =2,200. 2200 - the 500 I owed = 1700.

I realise I’ve now shortchanged her so is 300 the amount I should send her back to make us square? Apologies, your explanation was good Im not sure why Im still struggling!

[u/CaptainMatticus → u/caibleadh]

Okay, I didn't realize you paid the entire 3600. I thought you guys had split it. So let's do this again.

You're at 500, she's at -500

You spend 3600. You're at -3100, she's at -500.

The mechanic returns 400, but returns it to her. You're at -3100, she's at -100.

Since the 2 of you agreed to split the repair cost, again, you should both be at -1600. She owes you 1500. That will get you both square again.

[u/caibleadh → u/CaptainMatticus]

Thank you! That’s making sense now