Word Problem HELP!?

Question

A random sample of Americans eligible to vote in 2010 showed that 8% more people identified themselves as Independents rather than Republicans, and 6% fewer people identified themselves as Republicans than as Democrats. of those sampled, 2% did not identity with any of the three cate glories, What percent of the people in the sample identified themselves with each of the three political affilations? 

Answer 1

We are given

1. "8% more people identified themselves as Independents rather than Republicans"

 

Let R = # of Republicans; then R + 8 = % Independent

 

2. "6% fewer people identified themselves as Republicans than as Democrats"

 

Then %D = R - 6; rewriting R + 6 = %D

 

3. "2% did not identity with any of the three categories"

 

Since the sum of these percentages will be 100%, we can write

100% = 2% + (R + 8%) + (R + 6%) + R

100% = 2% + 14% + 3R

84% = 3R

28% = R

R + 8% = 36% (# of Independents), and R + 6% = 34% (# of Democrats)

We see that 36% + 34% + 28% + 2% = 100%