Discussion
The average age of all the students of a class is 16 years. The average age of boys is 21 years and that of girls is 12 years. If the number of girls in a class is 10, find the number of boys.
Answer: B
The number of boys is 8.
Let \(b\) be the number of boys. The total age of the class equals the boys' total plus the girls' total:
\[ \begin{aligned} 16(b + 10) &= 21b + 12 \times 10 \\ 16b + 160 &= 21b + 120 \\ 5b &= 40 \Rightarrow b = 8 \end{aligned} \]
Check: \(8 \times 21 + 10 \times 12 = 168 + 120 = 288\), and \(288/18 = 16\). The other values fail this check; for example 12 boys give an average of \((252 + 120)/22 \approx 16.9\).
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