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

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Math Expert
Joined: 02 Sep 2009
Posts: 55668
In a certain election race, all of the 8,400 votes were cast for eithe  [#permalink]

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13 Dec 2018, 01:15
00:00

Difficulty:

5% (low)

Question Stats:

98% (00:53) correct 3% (00:00) wrong based on 45 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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13 Dec 2018, 01:31
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

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Joined: 04 Jan 2015
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In a certain election race, all of the 8,400 votes were cast for eithe  [#permalink]

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13 Dec 2018, 04:31

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

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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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28 Dec 2018, 12:08
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   [#permalink] 28 Dec 2018, 12:08
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