July 2012 15

Question

In a village A the number of men equals the number of women.  The same is true for village B and also for village C. The number of men in village A plus the number of women in village B equal the number of women in village C. Six times the men of village  A plus three times the women in village B equals four times the women of village B. What is the population of each village?

Answer 1

Since the numbers of men and women are the same in each village, we only need three variables A, B, and C for the number of men OR women in each.  The populations of the villages are 2A, 2B and 2C.

 

The number of men in village A plus the number of women in village B equal the number of women in village C.

A+B = C

 

Six times the men of village A plus three times the women in village B equals four times the women of village B.

6A+3B = 4B

6A = B

 

Substitute in A+B = C

A+6A = C

C = 7A

 

Assuming A=1, then B=6 and C=7

The ratio of A to B to C is 1:6:7, or 2:12:14, etc.

The ratio is the best you can do.

You need one more piece of information somewhere to find the specific populations.

If you find something you left out and finish the solution, don't forget to double A, B and C to get the the whole village populations,