3.52 Adam Middle School and Baker Middle School students all took an exam. The average scores of boys and girls from these two schools are listed as follows: What is the average score of girls from both schools?
(A) 81.
(B) 82.
(C) 83.
(D) 84.
(E) 85.
(41st American High School Mathematics Examination, 1990)
[Solution] Let the number of male and female students at Yajie Middle School be $a, b$; and the number of male and female students at Beck Middle School be $c, d$. According to the problem, we have
$$
\left\{\begin{array}{l}
\frac{71 a+76 b}{a+b}=74, \\
\frac{81 c+90 d}{c+d}=84, \\
\frac{71 a+81 c}{a+c}=79 .
\end{array}\right.
$$

From (1), we have $3 a-2 b=0$, which means $b=\frac{3}{2} a$,
From (2), we have $3 c-6 d=0$, which means $d=\frac{1}{2} c$,
From (3), we have $8 a-2 c=0$, which means $c=4 a$.
Thus, $\frac{76 b+90 d}{b+d}=\frac{76 \cdot \frac{3}{2} a+90 \cdot \frac{1}{2} c}{\frac{3}{2} a+\frac{1}{2} c}=\frac{76 \cdot \frac{3}{2} a+90 \cdot 2 a}{\frac{3}{2} a+2 a}$ $=\frac{38 \cdot 3+180}{\frac{3}{2}+2}=84$.

Therefore, the answer is $(D)$.