Final answer:
The two coins that make up 55 cents without using a nickel are a half dollar and a nickel.
Step-by-step explanation:
To find out which coins make up 55 cents without using a nickel, we can use some logical reasoning. Since one of the coins is not a nickel, it means that the other coin must be a nickel. So, one of the coins is a nickel, which is worth 5 cents. To make up the remaining 50 cents we need a coin that is worth 50 cents.
The only coin in the options provided that is worth 50 cents is a half dollar. Therefore the two coins that make up 55 cents without using a nickel are a half dollar and a nickel. So the answer is option (C) A half dollar and a nickel.