The Distribution of Money Among Abraham, Sylvia, and Fred: A Mathematical Analysis

Imagine a scenario where a parent decides to distribute a sum of $13.50 among their three children, Abraham, Sylvia, and Fred. The distribution follows a unique pattern: Abraham receives twice as much as Sylvia, and Sylvia receives three times as much as Fred. How much money does each child receive? This article will walk you through the step-by-step mathematical analysis to solve this intriguing problem.

Introduction to the Problem

Given the sum of $13.50, we know the following relationships:

Abraham receives twice as much as Sylvia: ( A 2S ) Sylvia receives three times as much as Fred: ( S 3F ) Fred receives a certain amount of money: ( F )

Our goal is to find the amount of money each child receives, with a particular focus on Abraham.

Mathematical Analysis

First, let's establish the relationships mathematically:

1. Expressing All Variables in Terms of Fred's Amount (F)

We know that Sylvia's amount ( S ) in terms of Fred's amount ( F ) is:

S 3F

Abraham's amount ( A ) is twice Sylvia's amount, so:

A 2S 2(3F) 6F

Now, we can express the total amount of money distributed:

A S F 13.50

Substituting the expressions in terms of ( F ):

6F 3F F 13.50

Combining like terms:

10F 13.50

Solving for ( F ):

F frac{13.50}{10} 1.35

Thus, Fred receives $1.35.

2. Calculating Sylvia's Amount

Substituting ( F ) back into the equation for Sylvia's amount:

S 3F 3 times 1.35 4.05

So, Sylvia receives $4.05.

3. Calculating Abraham's Amount

Using Abraham's relationship with Sylvia:

A 2S 2 times 4.05 8.10

Therefore, Abraham receives $8.10.

Verifying the Solution

To verify our solution, we can check if the total sum adds up to $13.50:

8.10 (Abraham) 4.05 (Sylvia) 1.35 (Fred) 13.50

This confirms that our solution is correct and complete.

Conclusion

Through this problem, we have utilized algebraic relationships and logical steps to determine the exact amounts of money each child receives. Abraham receives $8.10, Sylvia receives $4.05, and Fred receives $1.35. This problem not only provides a practical application of algebra but also highlights the importance of understanding mathematical relationships in real-life scenarios.

keywords: money distribution, algebraic problem, equation solving