Deducing the Weight of the Glass: A Juice Puzzle

In the realm of logical puzzles and problem-solving, a seemingly simple question can unveil interesting mathematical insights. Consider this intriguing scenario: a glass full of juice weighs 1 kg, while half of the glass, containing half the juice, weighs 3/4 kg. The challenge here lies in determining the individual weights of the glass and the juice.

This puzzle, although trivial in nature, can be effectively solved by setting up simultaneous equations and using basic algebra. Let's delve into the solution and explore the underlying principles.

Setting Up the Equations

To tackle this problem systematically, let's define the variables: x: the weight of the glass (in kg) 2y: the weight of the full juice (in kg) We are given the following information:

The combined weight of the glass and the full juice is 1 kg:

x   2y  1

The combined weight of the glass and half the juice (which is equivalent to the weight of the glass plus one half of the full juice) is 3/4 kg:

x   y  0.75

Solving the Simultaneous Equations

Naturally, our next step is to solve these simultaneous equations. We can utilize either the elimination or substitution method. In this instance, the substitution method is straightforward and effective:

Step-by-Step Solution:

From the second equation, solve for y:

y  0.75 - x

Substitute this value of y into the first equation:

x   2(0.75 - x)  1x   1.5 - 2x  11.5 - x  1x  0.5

Once we have the value of x, it is easy to find y using the substitution method:

y  0.75 - xy  0.75 - 0.5y  0.25

Therefore, the weight of the glass is 0.5 kg (or 500 grams), and the weight of the full juice is 0.5 kg (or 500 grams).

The Significance

The method used to solve this puzzle is a fundamental application of algebra to real-life scenarios. Understanding how to set up and solve these types of equations can be invaluable in various fields, such as physics, engineering, and even in everyday problem-solving.

Conclusion

By breaking down the given problem into mathematical equations and solving them, we have successfully deduced the weight of the glass. This exercise serves as a reminder of the power of mathematics in unraveling mysteries and providing logical solutions to real-world problems.