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

1983 AMC 12 Problem 9

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In a certain population the ratio of the number of women to the number of men is

11

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

32\frac9{10}

32\frac{20}{21}

33

33\frac1{21}

33\frac1{10}

Use groups of

11

women and

10

men

Divide

11\cdot34+10\cdot32

by the total number of people

Using

11

women and

10

men, the total of all ages is

11\cdot34+10\cdot32=694.

Dividing by

21

people gives

\frac{694}{21}=33\frac1{21}.

Therefore, the correct answer is D.