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?

To solve this problem, we can use algebra to represent the value of the two coins.

Let's assume the value of the first coin is 'x' cents, and the value of the second coin is 'y' cents.

According to the given information, the total value of the two coins is 55 cents. This can be written as an equation:

x + y = 55

Now, let's consider that "one of the coins is not a nickel." In the United States, a nickel is worth 5 cents. So, we know that the first coin is not 5 cents. We can write this as:

x ≠ 5

To find the solution, we have to consider the possible values for 'x' and 'y' that satisfy both equations:

x + y = 55
x ≠ 5

Now, let's substitute the value of 'x' as 5 in the equation x + y = 55:

5 + y = 55

By subtracting 5 from both sides:

y = 55 - 5
y = 50

Therefore, the second coin is worth 50 cents. We have found both values:

First coin: x = 5 cents
Second coin: y = 50 cents

Therefore, one possible combination of coins that satisfies the conditions is a 5-cent coin and a 50-cent coin.