A Jar Is Filled With 22 Coins Consisting Of 2-rupee Coins And 5-rupee Coins. The Ratio Of The Number Of 2-rupee Coins To The Number Of 5-rupee Coins Is 5:1. There Are 245 2-rupee Coins In The Jar. How Many 5-rupee Coins Are In The Jar?
Introduction
Mathematics is a subject that deals with numbers, quantities, and shapes. It is a fundamental subject that is used in various fields such as science, engineering, economics, and finance. In this article, we will discuss a problem that involves the use of ratios and proportions to find the number of 5-rupee coins in a jar.
Problem Description
A jar is filled with 22 coins consisting of 2-rupee coins and 5-rupee coins. The ratio of the number of 2-rupee coins to the number of 5-rupee coins is 5:1. This means that for every 5 2-rupee coins, there is 1 5-rupee coin. There are 245 2-rupee coins in the jar. We need to find the number of 5-rupee coins in the jar.
Step 1: Understand the Ratio
The ratio of the number of 2-rupee coins to the number of 5-rupee coins is 5:1. This means that for every 5 2-rupee coins, there is 1 5-rupee coin. We can represent this ratio as a fraction: 5/1.
Step 2: Find the Number of 5-rupee Coins
We know that there are 245 2-rupee coins in the jar. We can use the ratio to find the number of 5-rupee coins. Since the ratio of 2-rupee coins to 5-rupee coins is 5:1, we can set up a proportion:
5/1 = 245/x
where x is the number of 5-rupee coins.
Step 3: Solve the Proportion
To solve the proportion, we can cross-multiply:
5x = 245
Now, we can divide both sides by 5:
x = 245/5
x = 49
Conclusion
Therefore, there are 49 5-rupee coins in the jar.
Real-World Applications
This problem has real-world applications in various fields such as finance, economics, and business. For example, in finance, the ratio of 2-rupee coins to 5-rupee coins can be used to represent the ratio of low-risk investments to high-risk investments. In economics, the ratio can be used to represent the ratio of consumer goods to capital goods.
Tips and Tricks
- When solving proportions, make sure to cross-multiply to avoid errors.
- When using ratios, make sure to understand the relationship between the two quantities.
- When solving problems involving ratios, make sure to check your units to ensure that they are consistent.
Common Mistakes
- Not understanding the ratio and its implications.
- Not checking units to ensure consistency.
- Not solving the proportion correctly.
Final Thoughts
In conclusion, this problem involves the use of ratios and proportions to find the number of 5-rupee coins in a jar. By understanding the ratio and using it to set up a proportion, we can solve the problem and find the correct answer. This problem has real-world applications in various fields and can be used to teach students about the importance of ratios and proportions in mathematics.
References
Q&A
Q: What is the ratio of 2-rupee coins to 5-rupee coins in the jar?
A: The ratio of 2-rupee coins to 5-rupee coins is 5:1.
Q: How many 2-rupee coins are in the jar?
A: There are 245 2-rupee coins in the jar.
Q: How many 5-rupee coins are in the jar?
A: To find the number of 5-rupee coins, we can use the ratio and the number of 2-rupee coins. Since the ratio of 2-rupee coins to 5-rupee coins is 5:1, we can set up a proportion:
5/1 = 245/x
where x is the number of 5-rupee coins.
Q: How do I solve the proportion?
A: To solve the proportion, we can cross-multiply:
5x = 245
Now, we can divide both sides by 5:
x = 245/5
x = 49
Q: What is the answer?
A: Therefore, there are 49 5-rupee coins in the jar.
Q: What is the significance of the ratio in this problem?
A: The ratio of 2-rupee coins to 5-rupee coins is 5:1, which means that for every 5 2-rupee coins, there is 1 5-rupee coin. This ratio is used to find the number of 5-rupee coins in the jar.
Q: How can I apply this concept to real-world problems?
A: This concept can be applied to real-world problems in finance, economics, and business. For example, in finance, the ratio of low-risk investments to high-risk investments can be represented by the ratio of 2-rupee coins to 5-rupee coins.
Q: What are some common mistakes to avoid when solving proportions?
A: Some common mistakes to avoid when solving proportions include:
- Not understanding the ratio and its implications
- Not checking units to ensure consistency
- Not solving the proportion correctly
Q: How can I improve my problem-solving skills?
A: To improve your problem-solving skills, you can:
- Practice solving proportions and ratios
- Review the concept of ratios and proportions
- Apply the concept to real-world problems
Conclusion
In conclusion, this problem involves the use of ratios and proportions to find the number of 5-rupee coins in a jar. By understanding the ratio and using it to set up a proportion, we can solve the problem and find the correct answer. This concept can be applied to real-world problems in finance, economics, and business.