Jannie Receives $R 150$ Pocket Money Per Month. In The New Year, His Mother Decided To Increase His Pocket Money In The Ratio $6:5$. Calculate Jannie's Adjusted Monthly Pocket Money.
Introduction
In this article, we will delve into the world of mathematics and explore a real-life scenario involving pocket money adjustments. Jannie, a young individual, receives a monthly stipend of R 150. However, his mother decides to increase his pocket money in a specific ratio. Our task is to calculate Jannie's adjusted monthly pocket money.
Understanding the Ratio
The ratio in which Jannie's pocket money is increased is 6:5. This means that for every 6 units of the original amount, 5 units are added to it. To understand this better, let's consider an example. Suppose Jannie's original pocket money is R 100. In this case, the ratio would be 6:5, which translates to 6 units of R 100 (R 600) and 5 units of the increase (R 500). The total amount would be R 600 + R 500 = R 1100.
Calculating the Increase
To calculate the increase in Jannie's pocket money, we need to find the difference between the original amount and the adjusted amount. Let's assume the original amount is R 150. We need to find the amount that is added to it in the ratio 6:5.
Step 1: Find the Total Parts of the Ratio
The total parts of the ratio are 6 + 5 = 11.
Step 2: Find the Value of 1 Part
To find the value of 1 part, we divide the original amount by the total parts of the ratio.
R 150 ÷ 11 = R 13.64 (approximately)
Step 3: Find the Increase
Now that we know the value of 1 part, we can find the increase by multiplying it by the number of parts that represent the increase (5).
R 13.64 × 5 = R 68.20 (approximately)
Step 4: Calculate the Adjusted Amount
Finally, we add the increase to the original amount to find the adjusted amount.
R 150 + R 68.20 = R 218.20 (approximately)
Conclusion
In conclusion, Jannie's adjusted monthly pocket money is approximately R 218.20. This is calculated by increasing his original pocket money of R 150 in the ratio 6:5.
Mathematical Formulation
For those who prefer a more mathematical approach, we can represent the problem as follows:
Let x be the original amount (R 150) and y be the increase (R 68.20). The ratio is 6:5, which can be represented as:
x + (6/11)x = y + (5/11)x
Simplifying the equation, we get:
(11/11)x + (6/11)x = (5/11)x + y
Combine like terms:
(17/11)x = (5/11)x + y
Subtract (5/11)x from both sides:
(12/11)x = y
Now, substitute the value of x (R 150) and solve for y:
(12/11) × R 150 = R 68.20 (approximately)
This confirms our previous calculation.
Real-World Applications
This problem may seem trivial, but it has real-world applications in various fields, such as finance, economics, and business. Understanding ratios and proportions is essential in making informed decisions and calculating adjustments.
Conclusion
Introduction
In our previous article, we explored the concept of adjusting pocket money in a specific ratio. We calculated Jannie's adjusted monthly pocket money using a step-by-step approach and a mathematical formulation. In this article, we will address some frequently asked questions related to this topic.
Q&A Session
Q: What is the original amount of Jannie's pocket money?
A: The original amount of Jannie's pocket money is R 150.
Q: What is the ratio in which Jannie's pocket money is increased?
A: The ratio in which Jannie's pocket money is increased is 6:5.
Q: How do we calculate the increase in Jannie's pocket money?
A: To calculate the increase, we need to find the difference between the original amount and the adjusted amount. We can do this by finding the value of 1 part of the ratio and multiplying it by the number of parts that represent the increase.
Q: What is the value of 1 part of the ratio?
A: The value of 1 part of the ratio is R 13.64 (approximately).
Q: How do we find the increase?
A: We find the increase by multiplying the value of 1 part by the number of parts that represent the increase (5). In this case, the increase is R 68.20 (approximately).
Q: What is the adjusted amount of Jannie's pocket money?
A: The adjusted amount of Jannie's pocket money is R 218.20 (approximately).
Q: Can we represent this problem mathematically?
A: Yes, we can represent this problem mathematically using the equation:
x + (6/11)x = y + (5/11)x
Where x is the original amount (R 150) and y is the increase (R 68.20).
Q: What is the significance of understanding ratios and proportions in real-life scenarios?
A: Understanding ratios and proportions is essential in making informed decisions and calculating adjustments in various fields, such as finance, economics, and business.
Q: Can we apply this concept to other real-life scenarios?
A: Yes, this concept can be applied to other real-life scenarios, such as calculating discounts, tips, or interest rates.
Conclusion
In this Q&A session, we addressed some frequently asked questions related to Jannie's pocket money adjustment. We hope this article has provided a better understanding of the concept and its applications in real-life scenarios.
Real-World Applications
Understanding ratios and proportions is essential in various fields, such as:
- Finance: Calculating interest rates, discounts, and tips
- Economics: Understanding supply and demand, inflation, and economic growth
- Business: Calculating profit margins, sales tax, and employee benefits
- Science: Understanding chemical reactions, physical laws, and biological processes
Conclusion
In conclusion, understanding ratios and proportions is a fundamental concept that has numerous applications in real-life scenarios. We hope this article has provided a better understanding of the concept and its applications.