Solving the Age Puzzle: A Fun Math Challenge

The age puzzle presented in this article involves a family consisting of Faye, a daughter named Ilana, and Faye's husband Leo. The puzzle requires us to deduce the ages of each member based on the given clues. While solving such puzzles can be challenging, they are fun and educational, especially for enhancing problem-solving skills in algebra and basic arithmetic. Let's break down the problem step-by-step and find the solution.

The Given Information

1. Faye is 31 years older than her daughter Ilana.

2. Faye is 2 years younger than her husband Leo.

3. The sum of their three ages is 100.

Mathematically, we can represent these statements as equations:

Faye's age (F) Ilana's age (I) Husband's age (H)

Step-by-Step Solution

Let's denote the ages of Faye, Ilana, and Leo as F, I, and H respectively.

From the given information, we have the following equations:

F I 31 H F 2 F H I 100

We can substitute the first two equations into the third equation to solve for I (Ilana's age).

Substitution and Simplification

H (I 31) 2 I 33 F H I 100 → (I 31) (I 33) I 100 3I 64 100 3I 36 I 12

Now that we have determined Ilana's age, we can find the ages of Faye and Leo.

Loading Up the Ages

Faye's age (F) 12 31 43 Husband's age (H) 43 2 45

To verify our solution, let's substitute these ages back into the original sum.

Verification

43 45 12 100

The solution checks out, confirming that Ilana is 12 years old, Faye is 43 years old, and Leo is 45 years old.

Additional Puzzles

Now that you have a clear understanding of the problem-solving process, let's try solving a similar age puzzle:

Let Ilana's age be x. Faye's age is x 31. Leo's age is x 33. The sum of their ages is 100.

Equation Setup

x (x 31) (x 33) 100

3x 64 100 3x 36 x 12

Therefore, Ilana is 12 years old, Faye is 43 years old, and Leo is 45 years old.

Conclusion

Age puzzles like this not only sharpen your algebraic skills but also build logical thinking. The key to solving such puzzles is to translate the given information into a set of equations and then systematically solve them. By practicing more puzzles, you can improve your problem-solving abilities and have fun with math.