Solving a Real-World Age Puzzle: Sarah and Henry's Story

In a classic word problem involving algebra, we are presented with a scenario about the ages of Sarah and Henry. This puzzle is not just a math problem but a fun way to apply algebraic concepts to solve real-world situations. Let's break down the problem and solve it step by step.

The Problem: Sarah and Henry's Age Riddle

The problem states: 'Sarah is four more than three times as old as Henry. In 8 years, the sum of their ages will be 92. How old is Sarah?' Let's translate this into algebraic expressions and solve it.

Step-by-Step Solution

We start by assigning variables to the ages of Sarah and Henry. Let H be Henry's current age and S be Sarah's current age. The first statement can be translated into the equation: S 3*H 4. The second statement can be translated into the equation: (S 8) (H 8) 92, which simplifies to S H 16 92 or S H 76. Now, we have a system of two equations: S 3*H 4 S H 76 We can substitute the first equation into the second equation to solve for H. Substituting S 3*H 4 into S H 76 yields: (3*H 4) H 76 4*H 4 76 4*H 72 H 18 Now that we know H 18, we can solve for S using the first equation: S 3*18 4 54 4 58 To verify our solution, we check the condition that in 8 years, the sum of their ages will be 92: Sarah's age in 8 years: 58 8 66 Henry's age in 8 years: 18 8 26 Sum of their ages in 8 years: 66 26 92 This verifies our solution is correct.

Conclusion

Therefore, Sarah is 58 years old, and Henry is 18 years old. This problem not only tests your understanding of algebraic concepts but also your ability to translate word problems into mathematical equations. Solving such problems can greatly enhance your algebraic and problem-solving skills.