Solving Age Problem Faraj And His Son's Present Age
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In the realm of mathematical puzzles, age-related problems often present intriguing challenges. These puzzles require careful analysis, logical deduction, and a systematic approach to unravel the relationships between individuals' ages at different points in time. This article delves into a classic age problem involving Faraj and his son, where we aim to determine the son's present age by deciphering the given information and employing algebraic techniques.
Decoding the Age Puzzle
Our age puzzle states: Faraj is thrice as old as his son. In seven years' time, the sum of their ages will be 50 years. The challenge lies in determining the son's present age. To solve this puzzle, we'll embark on a step-by-step journey, translating the word problem into mathematical equations and then solving for the unknown variable – the son's present age.
Establishing the Variables
The cornerstone of solving any mathematical problem is defining the variables. Let's assign the variable 'x' to represent the son's present age. Since Faraj is thrice as old as his son, Faraj's present age can be expressed as 3x.
Charting the Future Ages
The puzzle introduces a future time frame – seven years from now. To incorporate this information into our equations, we need to determine how the ages of Faraj and his son will change in seven years. In seven years, the son's age will be x + 7, and Faraj's age will be 3x + 7.
Forming the Equation
The puzzle states that in seven years, the sum of their ages will be 50 years. This crucial piece of information allows us to construct an equation. We simply add their ages in seven years and set the sum equal to 50: (x + 7) + (3x + 7) = 50.
Solving the Age Equation
With the equation in place, the next step is to solve for the unknown variable, 'x', which represents the son's present age. This involves a series of algebraic manipulations to isolate 'x' on one side of the equation.
Simplifying the Equation
Our equation is: (x + 7) + (3x + 7) = 50. The first step in simplification is to combine like terms. On the left side of the equation, we have 'x' and '3x', which combine to give '4x'. Similarly, we have '7' and '7', which combine to give '14'. Therefore, the simplified equation becomes: 4x + 14 = 50.
Isolating the Variable Term
The next step is to isolate the term containing the variable, '4x'. To do this, we subtract 14 from both sides of the equation: 4x + 14 - 14 = 50 - 14. This simplifies to: 4x = 36.
Solving for the Son's Age
Finally, to solve for 'x', we divide both sides of the equation by 4: 4x / 4 = 36 / 4. This yields the solution: x = 9. Therefore, the son's present age is 9 years.
Verifying the Solution
To ensure the accuracy of our solution, it's always a good practice to verify it by plugging the value of 'x' back into the original problem statement. Let's check if our solution satisfies the given conditions.
Faraj's Present Age
Since Faraj is thrice as old as his son, Faraj's present age is 3 * 9 = 27 years.
Ages in Seven Years
In seven years, the son's age will be 9 + 7 = 16 years, and Faraj's age will be 27 + 7 = 34 years.
Sum of Ages in Seven Years
The sum of their ages in seven years is 16 + 34 = 50 years, which matches the information given in the problem statement. This confirms that our solution is correct.
Conclusion
Through a systematic approach of defining variables, translating the word problem into equations, and employing algebraic techniques, we successfully determined the son's present age to be 9 years. This age puzzle highlights the importance of careful analysis, logical deduction, and the power of mathematical tools in solving real-world problems.
#additional-tips
Importance of Understanding the Problem
Before diving into equations, it's crucial to thoroughly understand the problem statement. Identify the unknowns, the given information, and the relationships between them. This understanding forms the foundation for setting up the equations correctly.
Step-by-Step Approach
Break down the problem into smaller, manageable steps. Define variables, express the given information in terms of these variables, form equations, and then solve them systematically. This step-by-step approach reduces complexity and minimizes errors.
Verification of Solution
Always verify your solution by plugging the obtained values back into the original problem statement. This ensures that the solution satisfies all the given conditions and eliminates any potential mistakes.
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Original Title
Faraj is thrice as old as his son. In seven years' time, the sum of their ages will be 50 years. What is the present age of the son?
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