Visual algebra puzzles involving balance scales are among the most engaging brainteasers on social media. Captions asking “What is the weight of one red ball?” encourage viewers to apply basic algebraic reasoning in a fun, visual way.
These puzzles rely on the concept of balanced equations: both sides of the scale weigh exactly the same amount.
Step-by-Step Mathematical Solution
To find the exact weight of a single red ball, let $r$ represent the weight of 1 red ball (in kg).
[ Balanced Scale Equation ]
|
+----------------------+----------------------+
| |
[ Left Scale Pan ] [ Right Scale Pan ]
- 6 Red Balls ($6r$) - 1 Red Ball ($1r$)
- 1 Weight block ($4\text{ kg}$) - 1 Weight block ($12\text{ kg}$)
1. Setting Up the Equation
By observing the items sitting on each pan of the balanced scale:
-
Left Pan: $6 \text{ red balls} + 4\text{ kg} \rightarrow 6r + 4$
-
Right Pan: $1 \text{ red ball} + 12\text{ kg} \rightarrow 1r + 12$
Since the scale is balanced, we set the two expressions equal to each other:
2. Solving for $r$
-
Step A: Subtract $1r$ from both sides to gather all terms with variables on the left side:
$$5r + 4 = 12$$ -
Step B: Subtract $4$ from both sides to isolate the variable term:
$$5r = 12 – 4$$$$5r = 8$$ -
Step C: Divide both sides by $5$ to solve for $r$:
$$r = \frac{8}{5} = 1.6\text{ kg}$$ -
Final Answer: 1.6 kg (or $1\frac{3}{5}\text{ kg}$)
Verification
To double-check the solution, plug $r = 1.6\text{ kg}$ back into both sides of the balance scale:
| Scale Pan | Calculation | Total Weight |
| Left Pan | $6(1.6) + 4 = 9.6 + 4$ | 13.6 kg |
| Right Pan | $1(1.6) + 12 = 1.6 + 12$ | 13.6 kg |
Both sides balance perfectly at 13.6 kg!
Key Takeaways and Conclusion
Visual scale puzzles are a great way to practice simple linear equations without needing complicated math setup. By cancelling out equal items from both sides (subtracting 1 red ball and 4 kg from each side), you quickly see that 5 red balls = 8 kg, making 1 red ball weigh 1.6 kg!
Frequently Asked Questions (FAQ)
What is the weight of one red ball?
One red ball weighs 1.6 kg (or 1,600 grams / $1\frac{3}{5}\text{ kg}$).
How do you solve scale balance puzzles?
Treat each side of the balance scale as an equation. Cancel out identical items or weights from both sides until you isolate a single unknown variable.
