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Math Help - Percentages

  1. #1
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    Percentages

    Hello all

    I have another percentages question that I think that you could help me with as it looks fairly basic but I am having trouble understanding the logic behind it.

    Q. What percentage of total eligible adults in the 1824 age category turned out to vote in Thundersley?

    a) 3.8% b) 6% c) 9.5% d) 12.8% e) 15%

    All the information is below in the table.

    Percentages-maths2.jpg

    Any help would be great.

    Cheers!
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  2. #2
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    Re: Percentages

    What exactly was your difficulty with this? The table says that 6% of the 18-24 voters turned out to vote in Thundersley.
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  3. #3
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    Re: Percentages

    Quote Originally Posted by HallsofIvy View Post
    The table says that 6% of the 18-24 voters turned out to vote in Thundersley.
    No, I think the table says that 6% of those who turned out to vote in Thundersley were in the 18-24 age category. Since we don't know from the table which share of the total population constitutes this age category, I don't see how we can answer the question.
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  4. #4
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    Re: Percentages

    Hi, I have just found the answer booklet and it suggests that the answer is A 3.8%. Does anybody know how they got this number? All the information is above.

    Many thanks
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  5. #5
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    Re: Percentages

    Well what I did was: in Thundersley, subtract the percentage of voters who did not vote from the total eligible, so 22,397 minus 36% of 22,397 is 14,334.08 voters who actually voted.

    Then 18-24 year olds were 6% of the total voters who did vote so the total amount of 18-24 year olds who voted is 6% of the 14,334.08 voters who did vote, which is 860.0448 18-24 year old voters.

    So what percent of all eligible voters (including ones who didn't vote) in Thundersley (22,397) were 18-24 year olds who did vote (860.0448 as we found earlier)?

    (x% of total possible voters 22,397 = 860.0448 18-24 year old voters)
    Last edited by daigo; July 4th 2012 at 07:36 AM.
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  6. #6
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    Re: Percentages

    Out of the Adults 36% did not vote at all

    100% of all elidgable voter munus that figure = 64% voted

    6 percent of 64% = 3.84
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  7. #7
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    Re: Percentages

    To avoid confusion, let's introduce some notation. We are talking about Thundersley only in this question. Let v_{\text{ac}} be the number of people in the age category ac who voted, and let e_{\text{ac}} be the number of eligible voters in the age category ac. For example, v_{\text{18-24}} is the number of people between 18 and 24 who voted, and e_{\text{18-24}} is the number of people between 18 and 24 who could have voted (maybe they did, maybe they didn't). Obviously, v_{\text{ac}}\le e_{\text{ac}} for each age category ac.

    Also, let

    e = e_{\text{18-24}} + e_{\text{25-34}} + e_{\text{35-44}}+e_{\text{45-54}}+e_{\text{55-74}}+e_{\text{75+}}

    be the total number of eligible voters and let

    v=v_{\text{18-24}} + e_{\text{25-34}} + v_{\text{35-44}}+v_{\text{45-54}}+v_{\text{55-74}}+v_{\text{75+}}

    be the total number of people who voted. Then the table provides the following facts:

    e=22,397

    v_{\text{18-24}} / e = 6\%

    v_{\text{25-34}} / e = 12\%

    ...

    v_{\text{75+}} / e = 4\%

    (e - v) / e = 36\%

    Since we know e, we can find v_{\text{ac}} for each category ac. However, we can't find e_{\text{ac}} for each ac because we don't know how people who didn't vote are distributed over the age categories. One possible scenario is that all eligible voters who did not vote are between 18 and 24. Then e_{\text{18-24}} = v_{\text{18-24}} + (e - v) = (6 + 36)\% of e, i.e., e_{\text{18-24}}=0.42\cdot22,397=9,407 people. Another scenario is that all eligible voters who did not vote are between 25 and 34. Then everybody who is eligible between 18 and 24 voted, i.e., e_{\text{18-24}} = v_{\text{18-24}} = 6\% of e, i.e., e_{\text{18-24}}=0.06\cdot 22,397=1,344 people.

    As far as I understand the question:
    Quote Originally Posted by lm320 View Post
    Q. What percentage of total eligible adults in the 1824 age category turned out to vote in Thundersley?
    it asks to find v_{\text{18-24}}/e_{\text{18-24}}. I don't think this question is answerable. Indeed, in the first scenario above, v_{\text{18-24}}/e_{\text{18-24}}=6/42=14\%, while in the second scenario v_{\text{18-24}}/e_{\text{18-24}}=100\%.

    I found the book "How to Pass Numerical Reasoning Tests" by Heidi Smith in Google Books. The answer 3.6% to this question appears on p. 190. It says,
    The percentage of all voting adults in Thundersley = 64%. 6% of 64% = 0.06 x 64 = 3.8% of eligible adults who voted were aged 18-24.
    However, this number is v_{\text{18-24}}/v and not v_{\text{18-24}}/e_{\text{18-24}}, for which the original question is asking.

    Quote Originally Posted by daigo View Post
    Well what I did was: in Thundersley, subtract the percentage of voters who did not vote from the total eligible, so 22,397 minus 36% of 22,397 is 14,334.08 voters who actually voted.

    Then 18-24 year olds were 6% of the total voters who did vote so the total amount of 18-24 year olds who voted is 6% of the 14,334.08 voters who did vote, which is 860.0448 18-24 year old voters.
    No, 18-24 year olds were 6% of the total eligible voters.

    Quote Originally Posted by daigo View Post
    So what percent of all eligible voters (including ones who didn't vote) in Thundersley (22,397) were 18-24 year olds who did vote (860.0448 as we found earlier)?
    The answer to this question is given in the table: 6%.
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    Re: Percentages

    Quote Originally Posted by emakarov View Post
    No, 18-24 year olds were 6% of the total eligible voters.
    I didn't think the graph clearly stated that, so I guess I read the graph incorrectly. Since all the voters in Thundersley add up to 64% (6% + 12% + 13% + 13% + 16% + 4%), and the people who didn't vote make up the remaining 36%, it would seem like the 6% of the total 100% which include those who didn't vote (6% + 12% + 13% + 13% + 16% + 4% + 36%) were 18-24 year olds.

    Quote Originally Posted by emakarov View Post
    The answer to this question is given in the table: 6%.
    See my reasoning above
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  9. #9
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    Re: Percentages

    Quote Originally Posted by daigo View Post
    Since all the voters in Thundersley add up to 64% (6% + 12% + 13% + 13% + 16% + 4%), and the people who didn't vote make up the remaining 36%, it would seem like the 6% of the total 100% which include those who didn't vote (6% + 12% + 13% + 13% + 16% + 4% + 36%) were 18-24 year olds.
    Yes, the fact that the percentages in the Thundersley row of the table add up to 100% made me also conclude that the first number is v_{\text{18-24}}/e, not v_{\text{18-24}}/v.
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