Here is the full math:
This is the given info, with Cork as C, and bottle as B:
C+B=4.10
B=C+4.00
So since we know what B is, we insert it into the first equation:
C+C+4=4.10
Combine the C:
2C+4=4.10
Subtract 4 from both sides:
2C=.10
Divide by 2 on both sides:
C=.05
I also thought .10 — until you really take it in that it says the bottle is 4.00 more than the cork, not actually 4.00