Election math question?

Question

The most recent Gallup poll shows a 45% - 45% tie between Obama and McCain.

They break this down further by demographic group.

The white vote is 37% - 52% Obama - McCain

The black vote is 93% - 2%

The hispanic vote is 58% - 31%

What is the demographic make up of the survey, i.e. what percentage of those surveyed are white, black and hispanic?

Answer 1

Let K be the total number of voters for Obama (or McCain, in this case they are the same).The data imply that

.37w+.93b+.58h=.52w+.02b+.31h

=.45w+.45b+.45h=K

This in turn implies

b = .3703703704*K, h = -.1410934744*K, w = 1.992945326*K. Since the number of hispanic voters cannot be negative, K must equal 0, and so must w+b+h, so it is impossible for this demographic result to occur using a positive sample.