Solving the Ages Puzzle: Western and Southern State College

Recently, a problem has been making its rounds on the internet—a problem so straightforward that it may have students and math enthusiasts alike scratching their heads. The problem revolves around two state colleges, Western State College and Southern State College, whose age relationship provides a simple yet intriguing puzzle. Let's delve into the details and solve this puzzle using some basic algebra.

The Ages of Western and Southern State Colleges

The problem states that Western State College is 18 years older than Southern State College. This is given as:

w s 18

Additionally, it mentions that Western State College is 2.5 times as old as Southern State College, which is expressed as:

w 2.5s

Setting Up the Equations

To solve this problem, we need to use both equations we have. The first equation represents the age difference, while the second equation represents the age relationship. We can set these two expressions for w equal to each other:

s 18 2.5s

Solving for Southern State College's Age

Let's solve this equation step by step to find the age of Southern State College, denoted as s: Subtract s from both sides: (s 18) - s 2.5s - s 18 1.5s

To isolate s, we divide both sides by 1.5:

18 ÷ 1.5 s

12 s

So, Southern State College is 12 years old.

Calculating the Age of Western State College

Now that we know Southern State College is 12 years old, we can find the age of Western State College using the first equation:

w s 18

w 12 18

w 30

This means Western State College is 30 years old.

Conclusion

Therefore, Western State College is 30 years old, and Southern State College is 12 years old.

Lessons Learned

This problem serves as a reminder of the power of algebra and the importance of setting up equations correctly when solving real-world problems. The approach to this puzzle involves a few simple steps: setting up the equations, solving for one variable, and then using that information to find the second variable.

It’s also worth noting that while this puzzle is straightforward, some students might find it challenging, especially if they haven’t been taught proper algebraic methods. If you come across a problem like this, don't hesitate to seek guidance or practice solving similar problems to build your algebra skills.

An interesting takeaway is the comparison between posting such problems and doing the math. While posting questions online can provide quick solutions, it’s essential to develop problem-solving skills and understand the underlying concepts.

Key Takeaways

Western State College is 30 years old. Southern State College is 12 years old. Algebra is a powerful tool for solving real-world problems. Developing strong problem-solving skills is crucial.

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Keywords: age problem, mathematical puzzle, algebraic solution