Solving Weight Puzzles: Equal Logic for Beginners

Weight puzzles can be intriguing and fun challenges, especially when they involve simple algebraic equations. In this article, we'll explore a few weight-related word problems and solve them using logical reasoning and basic algebra. By the end, you'll be able to tackle similar puzzles confidently.

Let's start with a problem involving two siblings, Bodo and Sharon, and see how we can solve it using mathematical equations. This will help us understand the process in a practical, step-by-step manner.

Problem Statement

Bodo weighs 160 pounds more than his sister Sharon. Their combined weight is 180 pounds. How many pounds does Bodo weigh?

Solution 1: Using Substitution and Basic Algebra

To solve this problem, let's introduce variables to represent the weights of Bodo and Sharon:

Step 1: Let the weight of sister Sharon (S) be (x) pounds.
Step 2: Then, the weight of Bodo (B) can be represented as (x 160) pounds, since Bodo is 160 pounds heavier than his sister.

Step 3: Their combined weight is given as 180 pounds, so we can write the equation:

(x (x 160) 180)

Step 4: Simplify the equation:

(2x 160 180)

Step 5: Subtract 160 from both sides:

(2x 180 - 160)
(2x 20)

Step 6: Divide both sides by 2:

(x 10)

So, Sharon weighs 10 pounds.

Step 7: Now, calculate Bodo's weight:

(B 10 160 170) pounds.

Therefore, Bodo weighs 170 pounds.

Solution 2: Visual Representation and Logical Reasoning

To make this more tangible, let's consider a visual representation and logical reasoning approach:

Step 1: Let the weight of sister Sharon (S) be (x) pounds.
Step 2: Let the weight of Bernard (B) be (x 100) pounds, assuming a similar structure to the previous problem.

Step 3: Their combined weight is 120 pounds, so:

(x (x 100) 120)

Step 4: Simplify the equation:

(2x 100 120)

Step 5: Subtract 100 from both sides:

(2x 120 - 100)
(2x 20)

Step 6: Divide both sides by 2:

(x 10)

So, Bernard weighs 110 pounds (reasoning similar to the original problem).

Returning to our main problem, Sharon weighs 10 pounds, and thus Bodo weighs 170 pounds.

Solution 3: Direct Equivalence and Multiple Steps

Let's break down the logic in a straightforward manner:

Step 1: Let the weight of Sharon be (x) pounds.
Step 2: Let the weight of Bernard be (x 160) pounds since he weighs 160 pounds more than Sharon.

Step 3: Their combined weight is 180 pounds, so:

(x (x 160) 180)

Step 4: Simplify the equation:

(2x 160 180)

Step 5: Subtract 160 from both sides:

(2x 180 - 160)
(2x 20)

Step 6: Divide both sides by 2:

(x 10)

So, Sharon weighs 10 pounds, and Bodo weighs 170 pounds.

Conclusion

Through these step-by-step solutions, we have demonstrated how to solve linear equations for weight-related problems. The key is to set up the correct equations and simplify them to find the solution. This problem-solving approach can be applied to various real-life scenarios, making it a valuable skill in both mathematics and daily life.

For more practice and to improve your problem-solving skills, consider exploring similar puzzles and equations. Remember, the more you practice, the better you'll become at tackling these types of problems.