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Of the votes cast on a certain proposal, 80 more were in favor of the

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Bunuel
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Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink] New post   24 Nov 2015, 10:31
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Of the votes cast on a certain proposal, 80 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)

(A) 480
(B) 400
(C) 300
(D) 240
(E) 160
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B
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink] New post   24 Nov 2015, 10:43
Bunuel wrote:
Of the votes cast on a certain proposal, 80 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)

(A) 480
(B) 400
(C) 300
(D) 240
(E) 160


Solution : Let x be no. of votes against the proposal. Then no. of votes in favor would be x+80 and total no. of votes would be 2x+80.
40%(2X + 80) = X ==> X=160.
Total no. of votes = 2(160) + 80 = 400

Option B
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink] New post   24 Nov 2015, 10:48
Let the total number of votes cast = T
Number of votes cast in favour of proposal = F
Number of votes cast against the proposal = A

F = A + 80 -- 1
Since , the number of votes against the proposal was 40 percent of the total vote
A= (40/100)*T = .4T -- 2
=> F = (60/100)*T = .6T -- 3

From equations 1 , 2 and 3 ,we get
.2T = 80
=> T= 400
Answer B
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink] New post   07 Dec 2015, 17:50
Let x be the total of votes cast, the solution we want.
Number of people against the proposal: \(\frac{40}{100}\) x
Number of people in favor: 1 - \(\frac{40}{100}\) x = \(\frac{60}{100}\) x

Since,
Bunuel wrote:
80 more were in favor of the proposal than were against it

that means 80 is the difference of the two percentages.
\(\frac{60}{100}\) x - \(\frac{40}{100}\) x = \(\frac{20}{100}\) x

\(\frac{20}{100}\) x = 80
x = 400
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink] New post   08 Dec 2015, 01:14
favour of proposal =x+80
against the proposal=x
total votes =2x+80
now,
.4(2x+80)=x
.8x+32=x
.2x=320
x=320/2=160=votes against
total votes =320+80=400
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink] New post   08 Dec 2015, 17:54
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Hi All,

This question can be solved by TESTing THE ANSWERS.

Under normal circumstances, we would start by TESTing Answer B or D first. Since B is the 'easier' value, we'll start there...

Answer B: 400 total votes

We're told that 40% of the total votes were votes AGAINST the proposal:
(.4)(400) = 160 votes against

So the remaining votes were in FAVOR of the proposal:
400 - 160 = 240 votes for

With these two numbers, the difference is 240-160 = 80, which is a MATCH for what we were told. Thus, this MUST be the answer.

Final Answer:
Show Spoiler
B


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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink] New post   09 Jan 2016, 02:36
Against = x
For = x+80

get proportion

x/x+x+80=4/10

10x=8x+320 => x=160, so total number = 160*2+80=400

B
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink] New post   09 Jan 2016, 03:16
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Bunuel wrote:
Of the votes cast on a certain proposal, 80 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)

(A) 480
(B) 400
(C) 300
(D) 240
(E) 160


Hi,
Although a relatively simpler Question, fast thinking can save time for slightly complex Qs later..
IF votes against are 40 %, votes for will be 60%.
the difference is 20% which is given as 80..
so total will be 80/20 * 100=400
B
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink] New post   23 Jan 2019, 05:15
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Bunuel wrote:
Of the votes cast on a certain proposal, 80 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)

(A) 480
(B) 400
(C) 300
(D) 240
(E) 160

\(? = t\left( {{\rm{total}}} \right)\,\,\,\,\left\{ \matrix{\\
\,{\rm{against}}\,\,\,{\rm{ = }}\,\,a\,\,\mathop = \limits^{{\rm{stem}}} \,\,{2 \over 5}t \hfill \cr \\
\,{\rm{for}}\,\,{\rm{ = }}\,\,t - a\,\,\mathop = \limits^{{\rm{stem}}} \,\,80 + a\,\,\, \Rightarrow 2a = t - 80 \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,2\left( {{2 \over 5}t} \right) = t - 80\,\,\,\, \Rightarrow \,\,\,{1 \over 5}t = 80\,\,\,\, \Rightarrow \,\,\,\left( {\rm{B}} \right)\)


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink] New post   27 Jan 2019, 19:27
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Bunuel wrote:
Of the votes cast on a certain proposal, 80 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)

(A) 480
(B) 400
(C) 300
(D) 240
(E) 160


We can let n = the total number of votes. Thus, 0.4n votes were against the proposal, and 0.6n votes were in favor of the proposal. We can create the equation:

0.6n - 0.4n = 80

0.2n = 80

n = 80/0.2 = 800/2 = 400

Answer: B
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Re: Of the votes cast on a certain proposal, 80 more were in [#permalink] New post   15 Sep 2021, 15:14
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Re: Of the votes cast on a certain proposal, 80 more were in [#permalink]
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