I feel silly asking this, but my head is clogged.
Last year, I had some people do some sales work for me on commission. There were two people at a time, and I paid one of them 50% of the total, and one of them got 10% of the total, or $50, whichever was more. I recorded the amounts they gave me, not the amounts I paid them. I feel like there ought to be a way to figure out the totals, and also the break point between the percent or the base sum for the second person.
Help a dumb sick brain out?
Does the “or $50, whichever was more” clause apply to both people, or just to the 10%er?
It sounds like it just applies to the 10%er. In that case, you can take the amount paid to the 50%er and double it to find the total.
Note that the 10%er switches from being paid the fixed $50 to being paid on percentage just when the total crosses $500.
Your question is a bit confusing, but I believe the following is a correct interpretation. You had two sales people: A = Mrs. 50% and B = Mr. 10%. They worked separately and each one gave you a specific amount of money which was what each one sold net of the commission they kept. You only know now these net numbers and wish to learn the totals.
If you ignore the “or $50 whichever was more”, this is easy. The total that A collected is exactly twice what you received and the total that B collected is 10/9 times the amount you received. (If you got $900, B must have collected $1000 and kept 10% or $100 leaving $900 for you.) I state this because I’m not sure if the $50 minimum applied to both A and B or just B from the way you worded it.
When the $50 minimum applies, you have to modify this. If A collected a total less than $100, she would keep $50 and give you what she collected less $50. So if you got less than $50 from A, the total collected was whatever you got + $50.
If B collected less than $500, he would have kept $50 and given you the rest. So if B gave you less than $450, then the total he collected was what you received + $50.
If I’m wrong and they were working jointly selling together, ask again.
Why don’t you make it easier on all of us, check your records, and tell us how much each of them gave you?
Bolding mine.
Your math is sound, but I believe you misunderstood the problem. The OP posits that the salespeople turned in the gross sales amount. Which the OP recorded. And the OP then refunded the appropriate commission to the two salesfolks. And did not record those payments. Those payments are the numbers he’s trying to reverse engineer. I say this because:
Bolding again mine.
And the more I re-read what the OP wrote, the less convinced I am that my interpretation is open-and-shut correct. My interpretation remains plausible, but OldGuy’s interpretation may well be correct instead.
Hey OP: please explain which is correct: Did the salesfolks compute & keep their own commission only sending you the net, or did they turn over the gross sales and you paid them back their commission? In other words, are the numbers you *do *have the sales amounts *before *or *after *deducting commission?
Sorry for the confusion. Head colds are terrible. I see where the issue is.
Two people worked at an event I was not personally at. At the end of the day, one person took 10% of the total or $50, whichever was greater, and one person took 50% of the total with no minimum. All I got was an envelope giving me MY total for the day, after they paid themselves. I trust them to have done this correctly. So I have “Thursday the 12th, $278” as my take and my only information. What I am looking for is the total take before they paid themselves.
If the total was at least $500, you would’ve received 10% of the total from the first person (at least $50) and another 50% of the total from the second person (at least $250), for 60% of the total overall (at least $300). But you got less than $300, so this situation didn’t occur.
Instead, the total must’ve been less than $500; you received $50 from the first person, and another 50% of the total from the second person. Thus, out of your $278, we must have that $228 of it came from the second person. That $228 was 50% of the total, so the total would’ve been twice that: $456.
So, if I got less than $300, then my total = 2(amount I received+50). Thanks, that makes sense. If I took more than $300, I should divide the total by .4, I think, since I paid out 60%?
Whoops, I misinterpreted things in my last post. Hold on…
Ah, I interpreted the percentages as the amount each person was giving you, rather than the amount they kept for themself. Let me rewrite on the accurate interpretation…
If the total was less than $500, the first person would’ve taken $50, and the second person would’ve taken 50% of the total, leaving 50% of the total - $50 for you (which will be less than $200).
But you got more than $200, so that’s not what happened.
Instead, since the total was at least $500, the first person must’ve taken 10% of the total and the second person must’ve taken another 50% of the total, leaving 40% of the total for you.
So, yes, you should divide $278 by 0.4 to get that the total was $695. The first person took $69.50 and the second person took $347.50, leaving you your $278.
Sorry about the confusion. As explained by the reasoning above, the cut-off point of interest is actually $200; if you receive less than $200, then, as you note, the total is 2(amount you received + $50), and if you receive at least $200, then as you note, the total is (amount you received)/0.4.
Thank you 
I will do much better record-keeping this year.
Just proving that here at Straight Dope, we can answer three to four times as many questions as were actually asked.
Three to four times as many questions and with five to six times as many answers. And that’s just the right ones; the wrong ones are even more plentiful. 
I’m still not convinced that I understand the question. I’m going to need more information about the compensation agreements you had with these employees.
My first impression is that you made a different agreement with each salesperson so that person A would sell $X worth of merchandise and take a commission of 0.5($X); and that person B would sell $Y worth of merchandise and take a commission of either 0.1($Y) OR $50 (whichever is greater).*
However, the answer you accepted from Indistinguishable suggests that the two employees worked as a team and pooled their receipts, which totaled $695; of this, Person A got to take home $347.50, and Person B got to take home $69.50.
While Indistinguishable’s solution does work from a mathematical standpoint, as a real-world outcome, it strikes me as a bit implausible. If we assume that both salespeople contributed roughly equally to the gross receipts, Person B is getting royally shafted (and presumably knows that).
How did you persuade Person B to agree to such an inequitable compensation plan?
*Unfortunately, this compensation plan does not have a unique solution, although the formula would be [0.5($X) + $Y] +$50 = $328 (Person B sold less than $500 of merchandise and pocketed $50, leaving $278 for the boss).