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The average weight of boys is 54 kg, the average weight of girls is 48 kg, and the overall average is 51 kg. If the number of girls is 59, what is the total number of students?

1. 138
2. 118
3. 128
4. 124

Correct answer: 118

Solution

Let the number of boys be $b$. Then total weight of boys = $54b$ and total weight of girls = $48 \times 59$. The overall average gives $\frac{54b + 48\cdot59}{b+59} = 51$, which solves to $b=59$ and total students $=118$.

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