Your Mom could have called Verizon, discussed this overage with them, and they probably could have worked something out whereby your plan gets raised to the 1400 minute plan and Verizon backdates it to cover the overage time, saving you some money.
However, it also appears that your 110 minutes of overage only cost an additional $49.95. Considering your sister used 120 minutes more than you, the overage was actually HERS, and she should have been required to pay the $50. You shouldn't have been penalized in any way, much less have had to pay the WHOLE bill. That's crap.
You need to print out the bill, take it to your Mom, and show her the numbers. If she has even basic math skills, she should see who was at fault, and can apportion blame accordingly.
If your Mom decides to coddle your sister and refuses to make her take stock of her usage, your Mom needs to call Verizon now (and it never hurts to see if they can do something about the back-dating even at this late date) and up your plan to the 1400 minute one. You'll get Friends & Family, which your sister can use for those 75 minute calls, and everybody wins (except that your sister doesn't learn her lesson.)
