On one side of a scale there is a 1-kg weight and half of a brick. On the other side there is one full brick. The scale is balanced. How many kg does the brick weigh? Try to present at least 2 methods to solving this problem.
How does this problem help to understand equality concept?
balance:
1kg+1B=2B
1kg=(2-1)B so one B is 1kg.
To solve this problem, we need to determine the weight of the brick. Let's go through two different methods to find the answer:
Method 1: Using Algebra
Let's denote the weight of the brick in kilograms as 'x'.
Given that one side of the scale has a 1-kg weight and half of a brick, and the other side has a full brick, we can set up an equation based on the equality of the two sides:
1 + 0.5x = x
To balance the scale, the total weight on both sides should be equal.
Simplifying the equation, we have:
1 = x - 0.5x
1 = 0.5x
x = 2
Therefore, the brick weighs 2 kilograms.
Method 2: Using Fractional Equivalent
Since the weight of half a brick is the same as the weight of a 1-kg weight, we can express this relationship as a fraction:
1 kg / 0.5 brick = 1 kg / 1 brick
To find the weight of one brick, we can multiply both sides of this equation by the weight of a full brick:
1 kg / 0.5 brick * 1 brick = 1 kg / 1 brick * 1 brick
Simplifying, we have:
1 kg = 1 brick
This confirms that the weight of the brick is 1 kilogram.
Understanding the Equality Concept:
This problem helps to understand the concept of equality by demonstrating that both sides of a balanced scale are equal in weight. It highlights the idea that when two sides of an equation hold the same value, the equation is true. In this problem, the equality lies in the fact that the weight on one side of the scale is equal to the weight on the other side. By solving the problem and finding that the weight of the brick is 1 kilogram, we can see that it balances out the 1-kg weight and half of a brick on the other side, resulting in equality.