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Beth received 3/10 of the votes cast in a certian election

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eybrj2
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Beth received 3/10 of the votes cast in a certian election [#permalink] New post   07 Mar 2012, 15:34
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Beth received 3/10 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?

A. 1/5
B. 2/7
C. 3/10
D. 7/20
E. 1/2
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B
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Bunuel
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Re: PT #11 PS 3 Q 16 [#permalink] New post   07 Mar 2012, 15:48
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eybrj2 wrote:
Beth received 3/10 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?

A. 1/5
B. 2/7
C. 3/10
D. 7/20
E. 1/2


Let the total votes be 10. Beth received 3 votes, other votes 10-3=7. In order to have received 1/2 of the votes she needed 5 votes so 2 more, which is 2/7 of the other votes.

Answer: B.
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Re: Beth received 3/10 of the votes cast in a certian election [#permalink] New post   10 Jan 2015, 09:43
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At first I got it totally wrong !!

Sum of fractions of the Total votes casted 1.

x+ 3/10=1/2
x=2/10=1/5 ..................... So, beth needs another 1/5 th the total vote casted.

Remaining Fraction = 1- 3/10 = 7/10

Required Fraction = (1/5)/(7/10) = 2/7



eybrj2 wrote:
Beth received 3/10 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?

A. 1/5
B. 2/7
C. 3/10
D. 7/20
E. 1/2
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Re: Beth received 3/10 of the votes cast in a certian election [#permalink] New post   12 Jan 2015, 21:29
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.................... Beth .................... Non Beth ................. Total

Initial votes..... \(\frac{3}{10}\) ....................... \(\frac{7}{10}\) ......................... 1 (Assumed)

Requirement...... \(\frac{3}{10} + \frac{2}{10} = \frac{5}{10}\) ..................... \(\frac{7}{10} - \frac{2}{10} = \frac{5}{10}\) ...... 1

\(Fraction = \frac{\frac{2}{10}}{\frac{7}{10}} = \frac{2}{7}\)

Answer = B
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Beth received 3/10 of the votes cast in a certian election [#permalink] New post   07 Feb 2020, 08:15
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eybrj2 wrote:
Beth received 3/10 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?

A. 1/5
B. 2/7
C. 3/10
D. 7/20
E. 1/2


Let's assign a "nice" value to the total number of votes cast.
We'll choose a number that works well with the given information.

Let's say that a total of 10 votes were cast.

Beth received 3/10 of the votes cast in a certain election
3/10 of 10 = 3.
So, Beth received 3 votes

What fraction of the OTHER votes cast would she have needed in order to have received 1/2 of the votes cast?
Receiving 1/2 of the votes would require Beth to get a total of 5 votes.
In other words, Beth would have needed 2 additional votes among the 7 people who didn't vote for her

Answer: 2/7 = B

Cheers,
Brent
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Re: Beth received 3/10 of the votes cast in a certian election [#permalink] New post   04 Mar 2020, 06:22
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eybrj2 wrote:
Beth received 3/10 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?

A. 1/5
B. 2/7
C. 3/10
D. 7/20
E. 1/2


We can let the total number of votes cast = 100. Thus, Beth received 30 votes, and she must receive 20 of the remaining 70 votes in order to have received 1/2 of the votes cast. Therefore, she must receive 20/70 = 2/7 of the remaining votes.

Answer: B
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Re: Beth received 3/10 of the votes cast in a certian election [#permalink] New post   28 Apr 2022, 12:22
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Let the number of votes cast in the election be 100.

Of these, votes received by Beth = \(\frac{3}{10}\) * 100 = 30.

Therefore, fraction of the other votes cast = \(\frac{7}{10}\) * 100 = 70

If Beth has to receive ½ of the total votes cast, she has to receive 50 votes. So, she needs another 20 votes of the 70 votes.

Therefore, fraction of the other votes cast, needed by Beth = \(\frac{20 }{ 70}\) = \(\frac{2 }{ 7}\).

The correct answer option is B.
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Beth received 3/10 of the votes cast in a certian election [#permalink] New post   04 May 2023, 07:55
ThatDudeKnows, Bunuel.

I solved the question in the following way:

\(\frac{30v}{100} +\frac{ 70v}{100} (\frac{x}{100}) = \frac{50v}{100}\)

If I solve the equation, the value I get for x is\(\frac{ 200}{7}\).

What am I doing wrong?

Thanks for your help!
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Beth received 3/10 of the votes cast in a certian election [#permalink] New post   04 May 2023, 08:08
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AntonioGalindo wrote:
ThatDudeKnows, Bunuel.

I solved the question in the following way:

\(\frac{30v}{100} +\frac{ 70v}{100} (\frac{x}{100}) = \frac{50v}{100}\)

If I solve the equation, the value I get for x is\(\frac{ 200}{7}\).

What am I doing wrong?

Thanks for your help!


AntonioGalindo

The x/100 in your initial equation should be x. We are being asked what we would need to multiply that 70v/100 by in order to arrive at the requisite number of votes, so no reason to divide that by 100.

More importantly, I think this is a great example of why using reasoning before diving into the math is a good idea. A cake is cut into 10 slices. You have 3 of them. You want 5 of them. You need 2 of the other 7. 2/7. No "real" math, no equations,...and no (well, minimal) chance of making a mistake like the one that you did.
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Re: Beth received 3/10 of the votes cast in a certian election [#permalink] New post   09 May 2023, 14:44
ThatDudeKnows wrote:
AntonioGalindo wrote:
ThatDudeKnows, Bunuel.

I solved the question in the following way:

\(\frac{30v}{100} +\frac{ 70v}{100} (\frac{x}{100}) = \frac{50v}{100}\)

If I solve the equation, the value I get for x is\(\frac{ 200}{7}\).

What am I doing wrong?

Thanks for your help!


AntonioGalindo

The x/100 in your initial equation should be x. We are being asked what we would need to multiply that 70v/100 by in order to arrive at the requisite number of votes, so no reason to divide that by 100.

More importantly, I think this is a great example of why using reasoning before diving into the math is a good idea. A cake is cut into 10 slices. You have 3 of them. You want 5 of them. You need 2 of the other 7. 2/7. No "real" math, no equations,...and no (well, minimal) chance of making a mistake like the one that you did.



Thank you ThatDudeKnows!
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Re: Beth received 3/10 of the votes cast in a certian election [#permalink]
09 May 2023, 14:44
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