Solving a Family Age Puzzle: A Girl, Her Brother, and Sister’s Ages

Diving into the world of algebra, let's explore a classic family age puzzle. The problem involves a girl who is one-third as old as her sister and eight years younger than her brother. The sum of their ages is 38 years. Solving this puzzle not only sharpens our algebraic skills but also provides a fun and engaging way to use mathematical equations.

Setting Up the Equations

We need to denote the ages of the girl, sister, and brother as G, S, and B respectively. From the information provided, we can set up the following equations:

G S/3 - The girl is one-third as old as her sister. G B - 8 - The girl is eight years younger than her brother. G S B 38 - The sum of their ages is 38.

Solving the Equations

Now, let's solve these equations step by step.

From equation 1: S 3G. From equation 2: B G 8. Substitute S and B into equation 3: 3G G G 8 38. This simplifies to: 5G 8 38. Subtracting 8 from both sides gives: 5G 30. Dividing both sides by 5 gives: G 6.

Now we can find the ages of her sister and brother.

S 3G 3 * 6 18. B G 8 6 8 14.

Thus, the ages are:

Girl: 6 years old. Sister: 18 years old. Brother: 14 years old.

Conclusion

The problem of determining the ages of a girl, her sister, and her brother using algebraic equations showcases the practical application of mathematical concepts. By breaking down the equations and solving them systematically, we can uncover the hidden ages in a fun and engaging puzzle. This not only enhances problem-solving skills but also demonstrates how equations can model real-world scenarios.

Additional Information

For further exploration, you can solve similar problems or create your own family age puzzles. The key to solving such puzzles lies in setting up the correct equations and then systematically solving them. This exercise not only improves your algebraic skills but also enhances your logical reasoning and analytical abilities.