Math question

I have a friend who has a magical ability where he is able to turn a stone into a dollar bill. He charges a service fee .06 cents for every stone he turns into a dollar bill. What my question is is how many stones would he have to turn in a dollar bill for the fee to become $95?

I messed up the question. The fee is .00006 cents and I wanted to know how many it would take to 99$

Ugh! The fee is 0096 cents.

.0006 cents

16.5 million stones.

That doesn’t seem right, are you sure?

fee = .0006 cents = .000006 dollars
99/.000006 = 16,500,000
there are 16.5M fees in 99 dollars

Well then I have a while to go. Alright, thank you.

I think the better question is “are you sure”

This sounds like one of those riddles where you have to take into account what the end product. Couldn’t your friend just skip the part where he has to find customers, convert stones and pocket the money? So, 95 stones?
I remember a similar riddle (well, not all that similar) I heard when I was a kid. “If John can make 1 cigarette from 7 cigarette butts, how many cigarettes does he get from 49 butts?”. The obvious answer being 7, but it’s actually 8 because he can make one more from those seven.

I can get it done for you for $92.50. I know a guy.

It doesn’t matter, because every two minutes the fee will change again.

Surely there should be some sort of volume discount, right? Seems wrong to pay the one-at-a-time rate for millions of something.

(I’ll concede that the “stone into dollar bill” service is kinda specialized - those who are good at it can typically charge what they want.)

Also, just double checking since this is commonly screwed up, but the fee is .0006 cents, not $0.0006, correct? I’m partly asking because in the OP, it started out as .06 cents, then got changed to .0006 cents, which, almost, to me looks like a translation of .06 cents to $0.0006. A fee of .06 cents would require 17 stone-to-dollar transformations before the magical friend makes even a penny off his fees. A fee of .0006 cents would require 1667 transformations before even a single penny is made.

While this is correct, the OP is asking about 95 dollars, not 99 dollars, so adjust numbers appropriately. 15,833,333.333 … So 15,833,334 to crest 95 dollars at .0006 cents, or 158,334 at $0.0006.

Those that are really good at it can turn a grain of sand into a Krugerrand.

I’m missing something that doesn’t directly appear to be about the math per se.

Why would the fee ever become $95? Why would the fee, which is .06 (or .0006 or whatever it finally ended up being stipulated as), ever become something other than what it started out as?

1st stone: becomes a $1 bill, service fee is (let’s say) .06
2nd stone: becomes a $1 bill, service fee is .06
3rd stone: becomes a $1 bill, service fee is .06


Did you (the OP) perhaps mean the service fee increases by .06 with each transaction?

Did you perhaps instead mean when does the cumulative profit come up to $95?

I interpreted the question to mean the last (as no other interpretation makes sense to me), but the OP should clarify.

The real question is why is the fee so low? Even at 6 cents per change, he’d have people lined up around the block with massive quantities of rocks to change. He wouldn’t have time to do anything else. Instead, charge somewhere over 95 cents per change (with a limit of 100 stones per day per customer) and it’ll reduce the customer level to something bearable while not reducing his net fees.

Post #2 changed it to $99.

With regard to changing the fee, I think you would need to take into account how laborious the transformation is. And the OP doesn’t tell us if it occurs instantly or if it takes an hour. In fact, why offer the service at all? Just do it yourself and keep the proceeds. But going with the hypothetical, 16.5 million is correct.

Another way of looking at it is that the guy is paying people to bring stones to him rather than having to go out and collect his own rocks. Since collecting and transporting the rocks what is probably a very short distance is not difficult, he shouldn’t pay very much at all. Hence my suggestion that he pay less than 5 cents/stone.