In a class there are 30 girls and 15 boys. The total average weight of the class is 47 kg. The total average weight of boys is 58 kg. Find the approximate average weight of the girls

Options

A. 32 kg
B. 42 kg
C. 52 kg
D. 35 kg

Answer

To find the approximate average weight of the girls in the class, we can follow these steps:

### Step 1: Gather the given data
- Number of girls = 30
- Number of boys = 15
- Total average weight of the class = 47 kg
- Average weight of boys = 58 kg

### Step 2: Calculate the total weight of the class
The total average weight of the class can be calculated using the formula:
\[ \text{Total weight of the class} = \text{Average weight of the class} \times \text{Total number of students} \]
Total number of students = Number of girls + Number of boys = 30 + 15 = 45

So, the total weight of the class is:
\[ \text{Total weight of the class} = 47 \times 45 = 2115 \text{ kg} \]

### Step 3: Calculate the total weight of the boys
Using the average weight of boys, we can find the total weight of the boys:
\[ \text{Total weight of boys} = \text{Average weight of boys} \times \text{Number of boys} \]
\[ \text{Total weight of boys} = 58 \times 15 = 870 \text{ kg} \]

### Step 4: Calculate the total weight of the girls
Now, we can find the total weight of the girls by subtracting the total weight of the boys from the total weight of the class:
\[ \text{Total weight of girls} = \text{Total weight of class} - \text{Total weight of boys} \]
\[ \text{Total weight of girls} = 2115 - 870 = 1245 \text{ kg} \]

### Step 5: Calculate the average weight of the girls
Finally, we can find the average weight of the girls using the total weight of the girls and the number of girls:
\[ \text{Average weight of girls} = \frac{\text{Total weight of girls}}{\text{Number of girls}} \]
\[ \text{Average weight of girls} = \frac{1245}{30} \approx 41.5 \text{ kg} \]

### Step 6: Round to the nearest whole number
Since the question asks for the approximate average weight, we round 41.5 kg to 42 kg.

### Final Answer
The approximate average weight of the girls is **42 kg**.

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