Question 6 of 19intermediate🔧 ApplyNumerical2 marks

The weight of a brick is 1 kg more than half its weight. What is the weight of the brick?

Correct Answer

Given: Let the weight of the brick be ww kg. Equation: w=w2+1w = \frac{w}{2} + 1 Solution: Subtract w2\frac{w}{2} from both sides: w−w2=1w - \frac{w}{2} = 1 Simplify: w2=1\frac{w}{2} = 1 Multiply by 2: w=2w = 2 kg

Verification: Half of 2 kg is 1 kg, and 1 kg more than half its weight (1 kg) equals 2 kg. Answer: The weight of the brick is 2 kg.

Exercise: Figure it Out (Section 2) | Q: 4 | (Page Page 17)
For More Understanding

Explanation

Let the weight of the brick be ww kg. According to the problem, the weight equals 1 kg more than half its weight: w=w2+1w = \frac{w}{2} + 1. Subtracting w2\frac{w}{2} from both sides: w2=1\frac{w}{2} = 1. Multiplying by 2: w=2w = 2 kg.

Solution Steps

  1. Step 1: Let weight = ww kg

  2. Step 2: Form equation: w=w2+1w = \frac{w}{2} + 1

  3. Step 3: Subtract w2\frac{w}{2} from both sides: w−w2=1w - \frac{w}{2} = 1

  4. Step 4: Simplify: w2=1\frac{w}{2} = 1

  5. Step 5: Multiply by 2: w=2w = 2 kg

PreviousNext