50 boxes with equal weights were loaded in a ship. 5 more boxes each weighing 105 kg were later added, making the average weight of all the 55 boxes as 95 kg. The weight of each of the 50 boxes first loaded is

Options

A. 98 kg
B. 94 kg
C. 95 kg
D. 92 kg

Answer

To find the weight of each of the 50 boxes that were first loaded onto the ship, we can follow these steps:

### Step 1: Define Variables
Let the weight of each of the 50 boxes be \( x \) kg.

### Step 2: Calculate Total Weight of the 50 Boxes
The total weight of the 50 boxes is given by:
\[ \text{Total weight of 50 boxes} = 50x \text{ kg} \]

### Step 3: Calculate Total Weight of the 5 Additional Boxes
The weight of each of the 5 additional boxes is 105 kg, so the total weight of these boxes is:
\[ \text{Total weight of 5 boxes} = 5 \times 105 = 525 \text{ kg} \]

### Step 4: Calculate Total Weight of All 55 Boxes
The total weight of all 55 boxes (50 original boxes + 5 additional boxes) is:
\[ \text{Total weight of 55 boxes} = 50x + 525 \text{ kg} \]

### Step 5: Calculate Average Weight of All 55 Boxes
The average weight of all 55 boxes is given as 95 kg. Therefore, we can write the equation for average weight:
\[ \text{Average weight} = \frac{\text{Total weight of 55 boxes}}{55} \]
Substituting the total weight:
\[ 95 = \frac{50x + 525}{55} \]

### Step 6: Solve for \( x \)
To eliminate the fraction, multiply both sides by 55:
\[ 95 \times 55 = 50x + 525 \]
Calculating \( 95 \times 55 \):
\[ 5225 = 50x + 525 \]
Now, subtract 525 from both sides:
\[ 5225 - 525 = 50x \]
\[ 4700 = 50x \]
Now, divide both sides by 50 to find \( x \):
\[ x = \frac{4700}{50} = 94 \text{ kg} \]

### Conclusion
The weight of each of the 50 boxes that were first loaded is \( 94 \) kg.

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