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In an election, candidate Smith won 52% of the total vote in [#permalink]

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25 Sep 2012, 05:35

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In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

Re: In an election, candidate Smith won 52% of the total vote in [#permalink]

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25 Sep 2012, 06:00

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thevenus wrote:

In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

Re: In an election, candidate Smith won 52% of the total vote in [#permalink]

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24 Feb 2015, 02:34

EvaJager wrote:

thevenus wrote:

In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

\(b\) - percent of the vote that candidate Smith win in County B In our case: \(\frac{A}{B}=\frac{3}{1}=\frac{52-b}{61-52}\), from which \(b = 25%.\)

Answer A.

Sounds reasonable. I couldn't quite get the denominator 61-52 for B. 61% is only the votes in A. 52% are total votes. So, if we subtract 52% (the total votes) from 61% (only votes from A) we should remain with votes from B?

Re: In an election, candidate Smith won 52% of the total vote in [#permalink]

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28 Feb 2015, 10:31

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thevenus wrote:

In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

Let total votes in County A = 3x. Let total votes in County B = x. Hence total votes in Count A & B together = 4x

Given that, 0.52(4x) = 0.61(3x) + n(x) So, 2.08x = 1.83x + nx So, n = 0.25 = 25% Hence option A

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Say there are a total of 100 votes. 100/4 = 25. Three parts of the 100 are in country A. So 75. Rest is in country B. Thus 25, A.

Wasn't quite sure, so this was an elevated guess, does this work? Or was it luck? :D

The answer selected by this user IGNORES the percents that we're meant to use, and it's essentially just 'dumb luck' that the user got the question correct.

Here's how you can TEST VALUES to get to the correct answer.

Since we have 3 times as many voters in Country A as in Country B, let's start there....

Country A = 300 voters Country B = 100 voters

We're told that the candidate won 61% of the votes in A and 52% of the votes in TOTAL. We're asked for the percent of votes that the candidate won in Country B. From this information, we can set up the following equation...

In an election, candidate Smith won 52% of the total vote in [#permalink]

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20 Nov 2017, 17:30

thevenus wrote:

In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

Re: In an election, candidate Smith won 52% of the total vote in [#permalink]

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21 Nov 2017, 02:47

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thevenus wrote:

In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

A.25% B.27% C.34% D.43% E.49%

We can let the number of votes cast in County B = x and thus the number of votes cast in County A = 3x. We can create the following equation where p = percent of vote candidate Smith won in County B:

0.61(3x) + (p/100)x = .52(3x + x)

61(3x) + px = 52(4x)

183x + px = 208x

183 + p = 208

p = 25

Answer: A
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