Finding the Amount of Money Each Has

Oct 13, 2025 by miodeya.com 72 views

Introduction

In this article, we will delve into a mathematical problem involving pocket money. Johnson and his brother have a certain amount of money, and we need to find out how much each of them has. The problem is presented as follows: Johnson has $\frac{1}{3}(x+5)$ as pocket money, and his brother has N 50 less than him. Altogether, they both have N 500. Our goal is to find the value of $x$ and the amount of money each of them has.

Understanding the Problem

Let's break down the problem and understand what is given and what needs to be found. We are given that Johnson has $\frac{1}{3}(x+5)$ as pocket money, and his brother has N 50 less than him. This means that the brother's pocket money is $\frac{1}{3}(x+5) - 50$ . We are also given that the total amount of money they both have is N 500.

Setting Up the Equation

To solve this problem, we need to set up an equation that represents the total amount of money they both have. We can do this by adding the amount of money Johnson has to the amount of money his brother has. This gives us the equation:

\frac{1}{3}(x+5) + \left(\frac{1}{3}(x+5) - 50\right) = 500

Simplifying the Equation

Now that we have set up the equation, we can simplify it by combining like terms. We can start by distributing the $\frac{1}{3}$ to both terms inside the parentheses:

\frac{1}{3}(x+5) + \frac{1}{3}(x+5) - 50 = 500

Next, we can combine the two terms with the $\frac{1}{3}$ :

\frac{2}{3}(x+5) - 50 = 500

Isolating the Variable

Now that we have simplified the equation, we can isolate the variable $x$ by adding 50 to both sides of the equation:

\frac{2}{3}(x+5) = 550

Next, we can multiply both sides of the equation by $\frac{3}{2}$ to get rid of the fraction:

x+5 = 825

Finding the Value of $x$

Now that we have isolated the variable $x$ , we can find its value by subtracting 5 from both sides of the equation:

x = 820

Finding the Amount of Money Each Has

Now that we have found the value of $x$ , we can find the amount of money each of them has. Johnson has $\frac{1}{3}(x+5)$ as pocket money, so we can plug in the value of $x$ to find his amount of money:

\frac{1}{3}(820+5) = \frac{1}{3}(825) = 275

His brother has N 50 less than him, so we can subtract 50 from Johnson's amount of money to find his brother's amount of money:

275 - 50 = 225

Conclusion

In this article, we solved a mathematical problem involving pocket money. We set up an equation that represented the total amount of money Johnson and his brother have, simplified it, isolated the variable $x$ , and found its value. We then used the value of $x$ to find the amount of money each of them has. The final answer is that Johnson has N 275 and his brother has N 225.

Final Answer

Johnson has N 275 and his brother has N 225.

Mathematical Concepts Used

Algebraic Manipulation: We used algebraic manipulation to simplify the equation and isolate the variable $x$ .
Fraction Operations: We used fraction operations to simplify the equation and isolate the variable $x$ .
Equation Solving: We used equation solving to find the value of $x$ and the amount of money each of them has.

Real-World Applications

This problem has real-world applications in finance and economics. It can be used to model real-world scenarios where individuals have different amounts of money and need to find the total amount of money they have. It can also be used to model scenarios where individuals have different rates of saving or spending.

Future Research Directions

Future research directions in this area could include:

Modeling Real-World Scenarios: Developing mathematical models to represent real-world scenarios where individuals have different amounts of money and need to find the total amount of money they have.
Analyzing Financial Data: Analyzing financial data to understand how individuals save and spend their money.
Developing Mathematical Tools: Developing mathematical tools to help individuals make informed financial decisions.
Frequently Asked Questions: Solving the Pocket Money Problem ===========================================================

Q: What is the problem about?

A: The problem is about Johnson and his brother having a certain amount of pocket money. Johnson has $\frac{1}{3}(x+5)$ as pocket money, and his brother has N 50 less than him. Altogether, they both have N 500. We need to find the value of $x$ and the amount of money each of them has.

Q: How do we set up the equation?

A: To set up the equation, we need to add the amount of money Johnson has to the amount of money his brother has. This gives us the equation:

\frac{1}{3}(x+5) + \left(\frac{1}{3}(x+5) - 50\right) = 500

Q: How do we simplify the equation?

A: We can simplify the equation by combining like terms. We can start by distributing the $\frac{1}{3}$ to both terms inside the parentheses:

\frac{1}{3}(x+5) + \frac{1}{3}(x+5) - 50 = 500

Next, we can combine the two terms with the $\frac{1}{3}$ :

\frac{2}{3}(x+5) - 50 = 500

Q: How do we isolate the variable $x$ ?

A: We can isolate the variable $x$ by adding 50 to both sides of the equation:

\frac{2}{3}(x+5) = 550

Next, we can multiply both sides of the equation by $\frac{3}{2}$ to get rid of the fraction:

x+5 = 825

Q: How do we find the value of $x$ ?

A: We can find the value of $x$ by subtracting 5 from both sides of the equation:

x = 820

Q: How do we find the amount of money each has?

A: We can find the amount of money each of them has by plugging in the value of $x$ into the equation for Johnson's pocket money:

\frac{1}{3}(820+5) = \frac{1}{3}(825) = 275

His brother has N 50 less than him, so we can subtract 50 from Johnson's amount of money to find his brother's amount of money:

275 - 50 = 225

Q: What are the final answers?

A: The final answers are that Johnson has N 275 and his brother has N 225.

Q: What mathematical concepts were used?

A: The mathematical concepts used in this problem include:

Algebraic Manipulation: We used algebraic manipulation to simplify the equation and isolate the variable $x$ .
Fraction Operations: We used fraction operations to simplify the equation and isolate the variable $x$ .
Equation Solving: We used equation solving to find the value of $x$ and the amount of money each of them has.

Q: What are the real-world applications of this problem?

A: This problem has real-world applications in finance and economics. It can be used to model real-world scenarios where individuals have different amounts of money and need to find the total amount of money they have. It can also be used to model scenarios where individuals have different rates of saving or spending.

Q: What are the future research directions in this area?

A: Future research directions in this area could include:

Modeling Real-World Scenarios: Developing mathematical models to represent real-world scenarios where individuals have different amounts of money and need to find the total amount of money they have.
Analyzing Financial Data: Analyzing financial data to understand how individuals save and spend their money.
Developing Mathematical Tools: Developing mathematical tools to help individuals make informed financial decisions.