math
posted by Alyssa .
In my hand, I have two United States Coins whose totatl value is 55 cents. However, one of the coins is not a nickel.

What is your question? Are we supposed to guess the two coins?
There was once a silver five cent piece struck in the US that was called a half dime. It was eventually (in 1873) repleced by the nickel.
That could be one of your two coins. You can guess the other one. 
In my hand, I have two United States Coins whose totatl value is 55 cents. However, one of the coins is not a nickel.
The two coins are a half dollar and a nickel.
The problem statement said that "one" of the coins was not a nickel. Nothing was said about the "other" coin not being a nickel. 
are the two coins a half dollar and five pennies?
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