Problem:
In a certain population, the ratio of the number of women to the number of men is 11 to 10. If the average (arithmetic mean) age of the women is 34 and the average age of the men is 32, then the average age of the population is
Answer Choices:
A. 32109​
B. 322120​
C. 33
D. 33211​
E. 33101​
Solution:
f(−x)=−x−1−x+1​=x+1x−1​=(x−1x+1​)1​=f(x)1​
Let w be the number of women, m the number of men. From the given, w =11x and m=10x for some x; also 34w is the sum of the ages of the women and 32 m is the sum for the men. Thus the average age for all is
11x+10x34(11x)+32(10x)​=2134⋅11+32⋅10​=21694​=33211​.
Note: except for the leftmost expression in the previous line, the computation of the average is the same computation one would do if there were exactly 11 women and 10 men.