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beth receive 3/10 of the votes cast in a certain election.

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beth receive 3/10 of the votes cast in a certain election. [#permalink] New post 18 Oct 2006, 16:09
beth receive 3/10 of the votes cast in a certain election. what fraction of the other votes cast would she have needed in order to have received 1/2 of the votes casted?

1/5
2/7
3/10
7/10
1/2
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Re: votes needed [#permalink] New post 18 Oct 2006, 17:14
lan583 wrote:
beth receive 3/10 of the votes cast in a certain election. what fraction of the other votes cast would she have needed in order to have received 1/2 of the votes casted?

1/5
2/7
3/10
7/10
1/2


3/10 + x =1/2

x=1/2-3/10= 5/10-3/10=2/10=1/5 A.
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 [#permalink] New post 18 Oct 2006, 18:14
Answer is 2/7.

Beth got 3/10 casted votes. Other votes casted = 7/10.

If beth get 2/7 votes of 7/10 other casted votes, it'll be 2/7*7/10 = 1/5

3/10 + 1/5 = 1/2.

Key here is "what fraction of the other votes cast would she have needed".
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Re: votes needed [#permalink] New post 18 Oct 2006, 18:32
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Let's assume there were 10 votes cast. To get 1/2 of the votes, she needs 2 more votes out of the remaining 7. So, she needs 2/7 votes to get 1/2 of all the votes cast.
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 [#permalink] New post 18 Oct 2006, 18:39
You guys are really helpful. I wish we could all see these tricks quickly.
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 [#permalink] New post 18 Oct 2006, 18:42
Rayn wrote:
You guys are really helpful. I wish we could all see these tricks quickly.


D'OH I had a feeling there was a trick. thx !
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 [#permalink] New post 18 Oct 2006, 19:23
B.

take 10 votes in total. and u solve it quickly.
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 [#permalink] New post 19 Oct 2006, 10:00
Let X be the total number of votes and N be the fraction that we are looking for:

3X/10 + N* (7X/10) = X/2

Solve for N, you will get 2/7
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 [#permalink] New post 19 Oct 2006, 13:16
Yeah B. Assume number of votes is 10. 3 gone and 7 remain. She needs 2 votes to get 1/2. (2/7)7 = 2.
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  [#permalink] 19 Oct 2006, 13:16
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