Solving Weight Puzzles: A Fun Mathematical Challenge

Weight puzzles can be a delightful way to engage in some fun and educational algebraic problem-solving. This article will take you through the process of solving a specific weight puzzle involving Bernard and his sister Betsy. We'll break down the solution step-by-step and provide the final answer.

The Problem Statement: Bernard and Betsy's Weight

The problem states that Bernard weighs 100 pounds more than his sister Betsy. Their combined weight is 120 pounds. Let's use some algebraic equations to solve who weighs what.

Solution 1: Step-by-Step Approach

Let's denote Betsy's weight by X pounds. Then, Bernard's weight is X 100 pounds. Since their combined weight is 120 pounds, we can set up the following equation:

X (X 100) 120

Now, let's solve this equation step-by-step:

Combine like terms: X X 100 120

Simplify: 2X 100 120

Subtract 100 from both sides: 2X 20

Divide both sides by 2: X 10

Therefore, Betsy weighs 10 pounds. Now, let's find Bernard's weight:

Bernard's weight 10 100 110 pounds

Solution 2: Simplified Approach

We can also use a more straightforward method by directly setting up the combined weight:

x (x 100) 120

Again, this simplifies to:

2x 100 120

And follows the same steps as above to get:

X 10

So, Betsy weighs 10 pounds, and Bernard weighs 110 pounds.

Solution 3: Using a Different Notation

In this approach, we denote Betsy's weight as xn and Bernard's weight as x 100nx. We then set up the equation:

xn (x 100nx) 120

This simplifies to:

(1 n)x 100nx 120

For simplicity, we can let n 1, giving us:

2x 100 120

Following the same algebraic steps as before, we find:

x 10

Therefore, Betsy weighs 10 pounds, and Bernard weighs 110 pounds.

The Final Answer

Betsy weighs 10 pounds, and Bernard weighs 110 pounds. This combination fits perfectly into the given conditions of the problem.

Understanding and solving these types of weight puzzles can be incredibly beneficial for developing algebraic thinking and problem-solving skills. Whether you're a student, a teacher, or simply someone who enjoys a good mental challenge, these puzzles offer a fun and engaging way to practice mathematics.