Weight of a bucket when filled fully with water is 17 kg. If the weight of the bucket when half filled with water is 13.5 kg, what is the weight of empty bucket?

Options

A. 12 kg
B. 8 kg
C. 10 kg
D. 7 kg

Answer

To find the weight of the empty bucket, we can set up the problem using algebra. Let's denote:

- \( x \) = weight of the empty bucket
- \( y \) = weight of the water when the bucket is full

From the problem, we have two scenarios:

1. The weight of the bucket when fully filled with water is 17 kg:
\[ x + y = 17 \quad \text{(Equation 1)} \]

2. The weight of the bucket when half filled with water is 13.5 kg:
\[ x + \frac{y}{2} = 13.5 \quad \text{(Equation 2)} \]

Now, we can solve these equations step by step.

### Step 1: Solve Equation 1 for \( y \)
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 17 - x \quad \text{(Equation 3)} \]

### Step 2: Substitute Equation 3 into Equation 2
Now, we substitute Equation 3 into Equation 2:
\[ x + \frac{17 - x}{2} = 13.5 \]

### Step 3: Clear the fraction
To eliminate the fraction, multiply the entire equation by 2:
\[ 2x + (17 - x) = 27 \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ 2x + 17 - x = 27 \]
\[ x + 17 = 27 \]

### Step 5: Solve for \( x \)
Now, isolate \( x \):
\[ x = 27 - 17 \]
\[ x = 10 \]

### Conclusion
The weight of the empty bucket is 10 kg.