Here's my best attempt. I have no proof for this, and while the solving path seems semi-plausible, the end result doesn't really. If the result is useless, I hope the ideas I had can at least help. At some point, with the assumptions I made, I just saw it as an interesting puzzle on its own (even if my assumptions are wrong), since it all worked out fairly nicely in the solving process.
Let's start with some wild assumptions :)
Watch dealers do something similar. They have the sale price in "plaintext", and the money they owe the dealer in a letter code. For the code, they use a secret 10-letter word with no repeating letters, labelling the letters of it 1234567890. E.g. if they use the word
MLKH would equal
If we assume this is somehow also the case for this store, we run into the first problem: We know the last given example had a price of \$7500, but both SP and CP has five letters. This can be explained away if we assume the first letter is some kind of meta information. Sometimes this may be a cost/profit ratio or other things. Source
Let's test this on the known examples
\$650 and \$7500 both have a 5 in them. If they use a secret word, we would have to encounter a duplicate letter in the appropriate positions. And we do on the SPs with the letter
S, as long as the first letter indeed is some meta information.
We'll conclude that
T=6, S=5, P=0, O=7, M=0, V=0. We'll also conclude that since they told you the value of the SP, the value of CP is less than SP for a given item because CP is the price "they don't want you to know", e.g. cost price or something similar. This hints towards a slightly different approach than the watchmakers. It looks like we have one 9 letter word labelled 1-9, and the rest of the alphabet just represents
0. We can already see that a substring of the secret word has to be
STO, since S=5, T=6 and O=7. Unfortunately, it can't be the substring
STORE because if
E=9, the CP of the last item would start with a
CP > SP, contradicting our assumption.
If you somehow still believe me at this point, we can make some deductions
We know the secret word is of the form
....sto... Now, we can assume the first (non-meta) letter of each price tag is not 0, otherwise it wouldn't be needed. Let's collect all the first digits of the known examples:
UCOLSBTE. So we know the secret word contains all of these 8 letters, and one unknown letter.
To further justify this, we can run a frequency analysis of all the given codes. The sample size is small, but nonetheless, you would expect letters that do not represent 0 to occur more often than a specific letter that does represent 0, since there are so many of them. The top 5 results (the ones which occur more often than 2x times) are indeed a subset of
UCOLSBTE. It's also noteworthy that it makes sense that
S is the most common one, since 5 is arguably the digit which gets used most for prices with no decimal points other than 0. (steps of 50/500, etc)
We can make some more deductions with this. We know that
CP < SP, and therefore: If both SP and CP of a given item have the same amount of letters, know that the value of the first letter of CP must be less than the value of the first letter of SP, otherwise CP would be higher than SP. E.g. with the first price tag
(A)UEUC vs (F)COSR, we can conclude that
U < C. Doing this for every item where CP & SP have the same amount of letters, we get the following 4 restrictions:
E < O
B < T
L < C
U < C
E < O: We know that we have the substring
STO taking up 5-7, therefore E must be between 1 and 4 (inclusive)
B < T: For the same reason as above, B must be between 1 and 4
L < C && U < C: Both L and U are less than C. Since the lowest values that E and B can have is 1&2, and thereby the lowest values L and U can have is 3&4, we know that C must be either 8 or 9, since 5 is already taken by S.
If you're still reading at this point
We could already make some good guesses at this point. Nonetheless I ran a quick dictionary search with the given criteria. And indeed, the only sensible combination that matched was
BLUE STOCK =
BLUESTOCK, giving the following map (all the remaining letters equal to 0):
The plainprice map would now be the one shown below. Unfortunately, this is where it all seems to crumble for real-life reasons. Unless the store is extremely over-priced, I don't see how e.g. an item that costs \$8500 has a cost price of \$2745. That would be insane. My best attempt at explaining myself at this point is that CP is not exactly the cost price, but something similar that's less than SP :) Or maybe the meta-letter has something to do with it...
| Item | CP | SP |
| 1 | 3438 | 8750 |
| 2 | 745 | 3705 |
| 3 | 2745 | 8500 |
| 4 | 700 | 5250 |
| 5 | 170 | 650 |
| 6 | 4960 | 7500 |