$1 \cdot 118$ Within a certain population range, the ratio of the number of females to the number of males is $11: 10$. If the average age of females is 34 years, and the average age of males is 32 years, then the average age within this population range is
(A) $32 \frac{9}{10}$.
(B) $32 \frac{20}{21}$.
(C) 33 .
(D) $33 \frac{1}{21}$.
(E) $33 \frac{1}{10}$.
(34th American High School Mathematics Examination, 1983)
[Solution] Let $w$ be the number of women, and $m$ be the number of men. Set $w=11 x, m=10 x$, and the total sum of the ages of all women is $34 w$, and the total sum of the ages of all men is $32 m$. Therefore, the overall average age is
$$
\frac{34(11 x)+32(10 x)}{11 x+10 x}=\frac{34 \cdot 11+32 \cdot 10}{21}=\frac{694}{21}=33 \frac{1}{21} \text{. }
$$

Therefore, the answer is $(D)$.