In a random sample of Americans of voting age, 7%
more people identified themselves as Independents than as Republicans, while 6%
fewer people identified themselves as Republicans than as Democrats. Of those sampled,
3%
did not identify with any of the three categories. What percent identified themselves with each of the three political affiliations?
To find the percentage of people who identified themselves with each political affiliation, we can start by assuming a total sample size of 100 people. Let's break down the problem step by step:
1. First, we have to identify the percentage of the sample that did not identify with any of the three categories. The problem states that 3% did not identify with any category. So, there were 100 * 3% = 3 people who did not identify with any political affiliation.
2. Next, we need to determine the percentage of people who identified themselves as Democrats. The problem states that there were 6% fewer people who identified as Republicans than Democrats. This means that the percentage of people who identified as Republicans is 6% less than the percentage of people who identified as Democrats. Therefore, the percentage of people who identified as Republicans is (100 - 6)% = 94% of the total sample size. Now, we need to consider that these Republicans are 7% fewer than Independents, so the percentage of Independents will be (94 + 7)% = 101% of the total sample size. Since the sum of the percentages exceeds 100%, we can conclude that 101% - 100% = 1% of the sample identified themselves as Independents.
3. Lastly, we need to determine the percentage of people who identified themselves as Republicans. We already found that 1% of the sample identified as Independents. As there were 7% more Independents than Republicans, the percentage of Republicans would be (1 - 7)% = -6% of the total sample size. However, we cannot have a negative percentage, so we'll consider that 0% of the sample identified themselves as Republicans.
To summarize:
- 3% of the sample did not identify with any of the three categories.
- 1% of the sample identified themselves as Independents.
- 0% of the sample identified themselves as Republicans.
- Therefore, the remaining 100 - (3 + 1 + 0)% = 96% identified themselves as Democrats.
Therefore, the percentages of people who identified themselves with each political affiliation are:
- Democrats: 96%
- Independents: 1%
- Republicans: 0%