Solving the Age Riddle: Karen and Lori's Ages
Introduction to the Riddle
Have you ever come across a math riddle that piques your curiosity? One such question involves figuring out the ages of two individuals based on a given relationship. In this article, we will explore a common age-related puzzle: Karen is twice as old as Lori, and together, their ages sum to 42. We will dive into the problem using multiple methods to ensure a clear understanding of the solution.
Method 1: Algebraic Approach
Let's denote Lori's age as (L) and Karen's age as (K). According to the riddle, we have the following two equations:
K 2L quad #35; (Karen is twice as old as Lori) K L 42 quad #35; (The sum of their ages is 42).
By substituting the first equation into the second equation, we can solve for (L)
2L L 423L 42frac{3L}{3} frac{42}{3}L 14.Now that we have Lori's age, we can find Karen's age using the first equation:
K 2L 2 times 14 28.
Thus, Karen is 28 years old.
Method 2: Using Ratios
Another way to approach this problem is by using ratios. Since Karen is twice as old as Lori, we can express the ratio of their ages as 2:1. If we denote Lori's age as (x) and Karen's age as (2x), the sum of their ages is expressed as:
2x x 423x 42frac{3x}{3} frac{42}{3}x 14 quad #35; Lori's age2x 2 times 14 28 quad #35; Karen's age.Verifying the Solution
To verify our solution, we can check if the sum of their ages is indeed 42:
14 28 42.
Additionally, we can confirm that Karen is twice as old as Lori:
28 2 times 14.
Both conditions are satisfied, so our solution is correct. This riddle demonstrates the power of algebra and ratios in solving real-world problems.
Conclusion
Understanding simple algebra and ratios can help you solve complex problems in a systematic and efficient manner. Whether you encounter age-related puzzles or other mathematical riddles, remember to break them down step-by-step and use the appropriate mathematical tools. Math is not just about numbers; it's a language that helps us understand the world around us.