551 used items, it takes 6 used to create one new... how many new items can you make? I had this question recently in an online exam that really confused me (it's not hard).

A business decided to recycle all their old paper cups and produce new ones from the recycled cardboard. For every new cup it would require $6$ used cups. They have $551$ used cups, how many new cups can be created?

I thought easy, divide $551$ by $6$ thus allowing the business to create $91$ new cups.
The answer was (according to the creator) $110$. Which is $551$ divided by $5$. I still can't wrap my head around the logic, I have written the question as I was given it, could anyone please help me shed some light on this?
 A: They can create $91$ new cups with $5$ used cups left over. After they use the $91$ cups, they’ll have $96$ used cups, from which they can create $\frac{96}6=16$ new cups with nothing over. After these are used, they’ll have $16$ used cups, from which they can create $2$ new cups with $4$ used cups left over. And finally, when the $2$ new cups have been used, they can make one more new cup from the $6$ used cups that they will then have. Along the way they’ve created a total of 
$$91+16+2+1=110$$
new cups. (But I think that the question is badly worded, perhaps deliberately so, in a way that disguises the fact that the answer is the long-term number of new cups, not the immediate number.)
A: at first you make $$\frac{551}{6} =91+ \frac{5}{6}$$ and having 5 rest. now we 96 paper cups that are 
$$\frac{96}{6}=16$$ 16, now we make 
$$\frac{16}{6}=2+\frac{4}{6}$$
$$\frac{6}{6}=1$$
so we have $$91+16+2+1=110$$
all together.
A: An easier way to see it: From 6 used cups they make 1 new one, so they are essentially using up 5 only (6 come in, 1 comes out). Thus 551/5 = 110.
