Solving the 30-Cent Coin Problem: One Coin is Not a Nickel
In the world of mathematics, there are many intriguing problems that challenge our logical thinking and problem-solving skills. One such classic problem is the "30-Cent Coin Problem," where you are given the following information:
"I have two U.S. coins that total 30 cents, and one of them is not a nickel."
The objective is to determine the two coins that make up this 30-cent total.
To solve this problem, we need to consider the possible combinations of U.S. coins that can add up to 30 cents, while ensuring that one of the coins is not a nickel.
The available U.S. coins and their respective values are:
- Penny: 1 cent
- Nickel: 5 cents
- Dime: 10 cents
- Quarter: 25 cents
Let's start by considering the possible combinations that can make up 30 cents:
- Two Dimes (10 cents each): 2 × 10 cents = 20 cents
- One Dime and One Quarter (10 cents and 25 cents): 10 cents + 25 cents = 35 cents
- Three Dimes (10 cents each): 3 × 10 cents = 30 cents
Now, we need to identify the combination where one of the coins is not a nickel.
The first option, two dimes, is a valid solution, as one of the coins is not a nickel.
The second option, one dime and one quarter, is not a valid solution because the quarter is a valid coin.
The third option, three dimes, is also not a valid solution because all three coins are dimes.
Therefore, the two coins that make up the 30-cent total, where one of them is not a nickel, are:
- 2 Dimes (10 cents each)
In conclusion, the solution to the "30-Cent Coin Problem" is that the two coins are two dimes, totaling 30 cents, with one of them not being a nickel.