Arjun Has Some 1-rupee Coins And 2-rupee Coins In His Piggy Bank. The Number 1-rupee Coins Is Thrice That Of 2-rupee Coins. If The Total Value Of These Coins Is ₹50, Find The Number Of Coins Of Each Denomination
Introduction
In this article, we will delve into a classic problem involving coins and mathematical reasoning. Arjun has a piggy bank containing 1-rupee coins and 2-rupee coins. The number of 1-rupee coins is thrice that of 2-rupee coins. We are tasked with finding the number of coins of each denomination, given that the total value of these coins is ₹50. This problem requires a combination of algebraic thinking and logical reasoning.
Understanding the Problem
Let's break down the problem and understand the given information:
- Arjun has 1-rupee coins and 2-rupee coins in his piggy bank.
- The number of 1-rupee coins is thrice that of 2-rupee coins.
- The total value of these coins is ₹50.
We need to find the number of coins of each denomination, i.e., the number of 1-rupee coins and the number of 2-rupee coins.
Setting Up the Equation
Let's assume the number of 2-rupee coins is x. Since the number of 1-rupee coins is thrice that of 2-rupee coins, the number of 1-rupee coins is 3x.
The total value of the coins is ₹50, which can be represented as:
2x + 3x = 50
Combine like terms:
5x = 50
Solving for x
To find the value of x, we need to isolate x on one side of the equation. Divide both sides by 5:
x = 50/5
x = 10
Finding the Number of Coins
Now that we have the value of x, we can find the number of 2-rupee coins and the number of 1-rupee coins.
The number of 2-rupee coins is x, which is 10.
The number of 1-rupee coins is 3x, which is 3(10) = 30.
Conclusion
In this article, we solved a classic problem involving coins and mathematical reasoning. We set up an equation based on the given information, solved for x, and found the number of coins of each denomination. The number of 2-rupee coins is 10, and the number of 1-rupee coins is 30.
Key Takeaways
- The problem requires a combination of algebraic thinking and logical reasoning.
- We set up an equation based on the given information and solved for x.
- We found the number of coins of each denomination by substituting the value of x into the equations.
Real-World Applications
This problem has real-world applications in finance and economics. For example, a business may have a mix of coins and bills in their cash register. By understanding the ratio of coins to bills, they can make informed decisions about their inventory and pricing.
Future Directions
This problem can be extended to more complex scenarios, such as:
- A mix of coins and bills with different denominations.
- A business with multiple locations and different inventory levels.
- A financial institution with a complex portfolio of assets and liabilities.
By exploring these extensions, we can develop a deeper understanding of mathematical reasoning and its applications in real-world scenarios.
References
- [1] Khan Academy. (n.d.). Algebra. Retrieved from https://www.khanacademy.org/math/algebra
- [2] Math Open Reference. (n.d.). Algebra. Retrieved from https://www.mathopenref.com/algebra.html
Glossary
- Algebra: A branch of mathematics that deals with the study of mathematical symbols, equations, and functions.
- Denomination: A unit of currency, such as a coin or bill.
- Inventory: A list of items, such as coins or bills, that a business has in stock.
- Pricing: The process of determining the cost of a product or service.
Frequently Asked Questions: Solving the Coin Problem =====================================================
Q: What is the main concept behind solving the coin problem?
A: The main concept behind solving the coin problem is to set up an equation based on the given information and solve for the unknown variable. In this case, we need to find the number of 2-rupee coins and the number of 1-rupee coins.
Q: How do we set up the equation for the coin problem?
A: To set up the equation, we need to understand the given information and translate it into mathematical terms. In this case, we know that the number of 1-rupee coins is thrice that of 2-rupee coins, and the total value of the coins is ₹50. We can represent this information as an equation: 2x + 3x = 50.
Q: What is the significance of the variable x in the equation?
A: The variable x represents the number of 2-rupee coins. By solving for x, we can find the number of 2-rupee coins, and then use that information to find the number of 1-rupee coins.
Q: How do we solve for x in the equation?
A: To solve for x, we need to isolate x on one side of the equation. In this case, we can divide both sides of the equation by 5 to get x = 50/5.
Q: What is the value of x in the equation?
A: The value of x is 10. This means that the number of 2-rupee coins is 10.
Q: How do we find the number of 1-rupee coins?
A: To find the number of 1-rupee coins, we can multiply the value of x by 3. In this case, we have 3(10) = 30, which means that the number of 1-rupee coins is 30.
Q: What are some real-world applications of the coin problem?
A: The coin problem has real-world applications in finance and economics. For example, a business may have a mix of coins and bills in their cash register. By understanding the ratio of coins to bills, they can make informed decisions about their inventory and pricing.
Q: Can the coin problem be extended to more complex scenarios?
A: Yes, the coin problem can be extended to more complex scenarios, such as:
- A mix of coins and bills with different denominations.
- A business with multiple locations and different inventory levels.
- A financial institution with a complex portfolio of assets and liabilities.
Q: What are some common mistakes to avoid when solving the coin problem?
A: Some common mistakes to avoid when solving the coin problem include:
- Not setting up the equation correctly.
- Not solving for the correct variable.
- Not checking the solution for reasonableness.
Q: How can I practice solving the coin problem?
A: You can practice solving the coin problem by:
- Working through example problems.
- Creating your own problems and solutions.
- Using online resources and practice tests.
Q: What are some additional resources for learning about the coin problem?
A: Some additional resources for learning about the coin problem include:
- Online tutorials and videos.
- Textbooks and study guides.
- Online communities and forums.
Conclusion
The coin problem is a classic example of a mathematical problem that requires algebraic thinking and logical reasoning. By understanding the concept behind the problem and practicing solving it, you can develop a deeper understanding of mathematical reasoning and its applications in real-world scenarios.