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In a school election involving three candidates, Ellen got e% of the

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In a school election involving three candidates, Ellen got e% of the [#permalink] New post   23 Apr 2020, 12:28
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In a school election involving three candidates, Ellen got e% of the votes, Fran got f% of the vote and Gayle got g% of the votes. If \(e=f+4\), \(f=g+5\) and 226 students vote for Ellen, how many votes were cast altogether?

(A) 400
(B) 450
(C) 500
(D) 550
(E) 600
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Re: In a school election involving three candidates, Ellen got e% of the [#permalink] New post   23 Apr 2020, 15:47
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g+g+5+g+9=100
Then we find Ellen got 85/300 or 52/150 votes which equals to 226. Therefore Fran got 48/150 and Gayle got 43/150.

Considering that Ellen's vote is not far beyond others, then it must be somewhere slightly below 226x3 and the number must be divisible by 300 or 150. The answer is E 600

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Re: In a school election involving three candidates, Ellen got e% of the [#permalink] New post   23 Apr 2020, 16:05
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assume total votes casted = x

Given-
\(e+e-4+e-9 = 100\)

\(e= \frac{113}{3} %\)

\(\frac{113}{300 } * x= 226 \)

x= 600




Ravixxx wrote:
In a school election involving three candidates, Ellen got e% of the votes, Fran got f% of the vote and Gayle got g% of the votes. If \(e=f+4\), \(f=g+5\) and 226 students vote for Ellen, how many votes were cast altogether?

(A) 400
(B) 450
(C) 500
(D) 550
(E) 600
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In a school election involving three candidates, Ellen got e% of the [#permalink] New post   24 Apr 2020, 14:56
nick1816 how did you get this e+e-4+e-9
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Re: In a school election involving three candidates, Ellen got e% of the [#permalink] New post   24 Apr 2020, 15:09
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e= f+4
f= e-4

Also, f=g+5

g=f-5
g=e-4-5 = e-9

As, there are only 3 candidates, e+f+g= 100 or e+e-4+e-9 = 100

dave13 wrote:
nick1816 how did you get this e+e-4+e-9
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Re: In a school election involving three candidates, Ellen got e% of the [#permalink] New post   25 Apr 2020, 15:07
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Ravixxx wrote:
In a school election involving three candidates, Ellen got e% of the votes, Fran got f% of the vote and Gayle got g% of the votes. If \(e=f+4\), \(f=g+5\) and 226 students vote for Ellen, how many votes were cast altogether?

(A) 400
(B) 450
(C) 500
(D) 550
(E) 600


Since the total percent of the votes is 100, we can create the equation:

e + f + g = 100

Since f = e - 4 and g = f - 5 = e - 4 - 5 = e - 9, we have:

e + e - 4 + e - 9 = 100

3e -13 = 100

3e = 113

e = 113/3

Letting n = the total number of votes cast, we can create the equation:

e/100 = 226/n

(113/3)/100 = 226/n

113/300 = 226/n

226/600 = 226/n

600 = n


Answer: E
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Re: In a school election involving three candidates, Ellen got e% of the [#permalink] New post   31 Jan 2024, 13:10
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Re: In a school election involving three candidates, Ellen got e% of the [#permalink]
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