The image shows a balancing scale with two pans, each holding a different combination of weights and red balls. The puzzle is simple yet captivating, designed to test your understanding of balance, algebra, and logical reasoning. The challenge is to determine the weight of a single red ball.

Breaking Down the Image

• Left Pan:
  • Contains 3 red balls.
  • A 4 kg weight block.
• Right Pan:
  • Contains 1 red ball.
  • A 10 kg weight block.

Despite their differences, the two pans balance each other perfectly, meaning the total weight on both sides is equal.

Step 1: Setting Up the Equation

To find the weight of a single red ball, let’s denote the weight of one red ball as $x$ kg.

The total weight on the Left Pan is the sum of the weights of the 3 red balls and the 4 kg block: $3x+4\text{ kg}$

The total weight on the Right Pan is the sum of the weight of 1 red ball and the 10 kg block: $x+10\text{ kg}$

Since the scale is balanced, the weights on both sides are equal: $3x+4=x+10$

Step 2: Solving the Equation

Now, solve for $x$ to find the weight of a single red ball:

1. Subtract $x$ from both sides to get all the $x$-terms on one side: $3x-x+4=10$
2. Simplify the equation: $2x+4=10$
3. Subtract 4 from both sides to isolate the $x$-term: $2x=6$
4. Divide both sides by 2 to solve for $x$: $x=3$

Conclusion: The Weight of the Red Ball

The solution reveals that each red ball weighs 3 kg.

This puzzle is an excellent example of how simple algebraic reasoning can be used to solve real-world problems. The challenge not only tests your mathematical skills but also encourages logical thinking and the application of basic principles in a practical scenario. Whether you’re a student or a puzzle enthusiast, this type of riddle is both fun and educational, providing a satisfying sense of achievement when you arrive at the correct solution.