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In a certain election race, all of the 8,400 votes were cast for eithe

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In a certain election race, all of the 8,400 votes were cast for eithe  [#permalink]

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New post 13 Dec 2018, 00:15
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

98% (00:48) correct 3% (00:00) wrong based on 40 sessions

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In a certain election race, all of the 8,400 votes were cast for either candidate A or candidate B. If votes for candidate A and votes for candidate B were cast in a 4 to 3 ratio, how many votes were cast for candidate A?

A. 1,200
B. 2,400
C. 4,800
D. 6,000
E. 8,400

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Re: In a certain election race, all of the 8,400 votes were cast for eithe  [#permalink]

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New post 13 Dec 2018, 00:31
Bunuel wrote:
In a certain election race, all of the 8,400 votes were cast for either candidate A or candidate B. If votes for candidate A and votes for candidate B were cast in a 4 to 3 ratio, how many votes were cast for candidate A?

A. 1,200
B. 2,400
C. 4,800
D. 6,000
E. 8,400



A:B = 4:3.


8400/ 7 * 4
= 4800

C is the answer.
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In a certain election race, all of the 8,400 votes were cast for eithe  [#permalink]

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New post 13 Dec 2018, 03:31

Solution


Given:
    • Total number of votes casted = 8400
    • Ratio of votes casted for candidate A to candidate B = 4: 3

To find:
    • The number of votes casted for candidate A

Approach and Working:
    • We know that A + B = 8400 ……. (1)
    • And, \(\frac{A}{B} = \frac{4}{3}\)
      o This implies, \(B = \frac{3A}{4}\)

Substituting in equation (1), we get,
    • \(A + \frac{3A}{4} = 8400\)
    • \(\frac{7A}{4} = 8400\)
    • Thus, \(A = \frac{(4 * 8400)}{7} = 4800\)

Therefore, the number of votes casted for candidate A = 4800

Hence, the correct answer is Option C

Answer: C

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Re: In a certain election race, all of the 8,400 votes were cast for eithe  [#permalink]

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New post 28 Dec 2018, 11:08
4 - candidate A
3 - candidate B

So votes of candidates combined is 7.

Hence, the ratio of votes for candidate A compared to the total amount of votes is:

4:7

So 4/7th out of the 8400, would give us the total amount of votes for candidate A.

4/7 * 8400 = 4800.
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Re: In a certain election race, all of the 8,400 votes were cast for eithe &nbs [#permalink] 28 Dec 2018, 11:08
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