Hey, dear Hyborians,
This one might be a language thing, but I really don’t understand what the wealthy skill (within the society tree) does and how it works. I’d really appreciate any help 
Hello! My two cents in case it helps:
I believe this refers back to making Society tests when attempting to find a piece of equipment to buy during the Upkeep and Carousing phase (page 135 of the Core book has the rules around purchasing new stuff). Having this talent would allow you to spend Momentum generated on that test to then not only find, but pay a lower than usual price for that item.
So for example I am going to make a Difficulty 2 Society test to find some item or other. If I succeed with 3 Successes (1 left over as Momentum), I can find the item and obtain it for 1 fewer Gold than normal if I choose to spend the Momentum to do so (I could pay normal price and just bank the Momentum instead).
From a narrative perspective, the cost “went down” in terms of what comes out of your character’s Gold tally because you were able to obtain additional funds from one of your secret stashes of wealth to cover, as I read it.
EDIT: fixed the page number reference.
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Thank you very much, this clarifies my problem! I totally overlooked that players have to roll for finding and buying equipment
To further clarify, the Wealthy Talent expresses that this provides bonus Momentum per Rank in Wealthy.
Please note that Momentum generated on any Society test used while hunting for Equipment already can reduce the cost in Gold per point of generated Momentum (p. 136), so my reading of the Wealthy Talent is that success at all would then provide the Momentum generated via this Talent.
So, say you make a D1 Test, generating two Successes, but you have two Ranks in Wealthy. Instead of generating just one Momentum, you have generated two more for the express cost of any purchase. You can use all three Momentum to reduce the cost by 3 (to a minimum of 1 Gold), or use just the two from the Talent, using the 1 Momentum as normally generated for some other purpose, if desired.
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Glad it helped and many thanks to Gebir for the reminder around it being bonus momentum as well - cheers!
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Well then, you are both awesome! Thank you very, very much. I must add, the Conan 2d20 community are great people, nice to hang around with you all!