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Last year, all registered voters in Kumannia voted either

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Last year, all registered voters in Kumannia voted either  [#permalink]

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New post 17 Dec 2009, 14:58
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Last year, all registered voters in Kumannia voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of revolutionary voters increased 10%, while the number of Status Que voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?
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Re: Kumannia  [#permalink]

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New post 21 Dec 2009, 09:39
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umaa wrote:
Last year, all registered voters in Kumannia voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of revolutionary voters increased 10%, while the number of Status Que voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?


Set the equation for the number of total voters this year: \(1.1R+1.05S=1.08(R+S)\) --> \(2R=3S\)

The question is \(\frac{1.1R}{1.1R+1.05S}=?\) --> \(\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}\). Now, as \(2R=3S\) then \(70R=105S\) (multiplying by 35) --> substitute 105S by 70R: \(\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}\)

Hope it's clear.
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Re: Kumannia  [#permalink]

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New post Updated on: 18 Dec 2009, 07:26
Can you use the alligation method here?

If voters of the Revolutionary party increased 10% and the Status Quo Party increased 5% and the overall total votes increased 8% then the Revolutionary party accounted for 60% of the vote.

R-------Average--------S
+10 +8 +5
(2 away from mean) (3 away from mean)
So

R/(R+S) = (3/5) or 60%.

Is this correct?

Originally posted by adamsmith2010 on 17 Dec 2009, 15:05.
Last edited by adamsmith2010 on 18 Dec 2009, 07:26, edited 1 time in total.
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Re: Kumannia  [#permalink]

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New post 17 Dec 2009, 20:07
revolutionary voter=r
status quo voter=s
total=t
t=r+s---->s=t-r

new r=1.1r
new s=1.05s
new t=1.08 t
---->1.1r+1.05s=1.08t
--->1.1r+1.05(t-r)=1.08t
--->.05r=.03t
---->r=3/5t

OA pls
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Re: Kumannia  [#permalink]

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New post 21 Dec 2009, 09:07
Even I've got 60%. But the answer is 11/18.
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Re: Kumannia  [#permalink]

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New post 21 Dec 2009, 09:58
1
11/18

1.1x+1.05y=1.08(x+y)
.02x=.03y
2x=3y (thought just it out there for more visually charged people like me).

1.1x/1.1x+1.05(2/3)x
(after drowning with decimals)

11/18
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Percents and voters  [#permalink]

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New post 26 Jul 2010, 17:55
Last year all the voters of a country voted for party A or party B. This year the number of voters voiting for A increased by 10% while the voters for party B increased by 5%. If the total number of voters increased by 8% what fraction of voters voted for party A this year.
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Re: Percents and voters  [#permalink]

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New post 26 Jul 2010, 20:08
Hi,

Let x be the percentage that voted for A and (100-x) the percentage who voted for B.

we have 1.1x + 1.05(100-x) = 8
Solving for x we get x = 60 (who voted for A) and (100-60) who voted for B.


regards,
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Re: Percents and voters  [#permalink]

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New post 26 Jul 2010, 21:39
1
Jinglander wrote:
Last year all the voters of a country voted for party A or party B. This year the number of voters voiting for A increased by 10% while the voters for party B increased by 5%. If the total number of voters increased by 8% what fraction of voters voted for party A this year.


Let a be the number of voters who voted for party A and be the number of voters who voted for party B last year.
Party A | Party B
--------------------------
a | b <---- Last yr
1.1 a | 1.05 b <-----This yr

The question also states that the total voters increased by 8% this year. So
1.1a + 1.05b = 1.08(a+b) => b =(2/3)*a

We need to find the fraction of voters who voted for party A this year i.e 1.1a/(1.1a + 1.05b)
= 1.1a/(1.1a + 1.05*(2/3)*a) = 1.1/1.8 =11/18
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Re: Kumannia  [#permalink]

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New post 08 Sep 2010, 08:29
Yes, 1.1/1.8 = 11/18
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Re: Kumannia  [#permalink]

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New post 17 Feb 2013, 15:00
Bunuel wrote:
umaa wrote:
Last year, all registered voters in Kumannia voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of revolutionary voters increased 10%, while the number of Status Que voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?


Set the equation for the number of total voters this year: \(1.1R+1.05S=1.08(R+S)\) --> \(2R=3S\)

The question is \(\frac{1.1R}{1.1R+1.05S}=?\) --> \(\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}\). Now, as \(2R=3S\) then \(70R=105S\) (multiplying by 35) --> substitute 105S by 70R: \(\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}\)

Hope it's clear.


I wish I could Kudos Bunuel's explanation a thousand times. I have found MGMAT's explanation of this problem, with their whole chart approach, almost indecipherable. Thank you for the clarity Bunuel!
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Re: Kumannia  [#permalink]

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New post 22 Nov 2013, 06:09
Bunuel wrote:
umaa wrote:
Last year, all registered voters in Kumannia voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of revolutionary voters increased 10%, while the number of Status Que voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?


Set the equation for the number of total voters this year: \(1.1R+1.05S=1.08(R+S)\) --> \(2R=3S\)

The question is \(\frac{1.1R}{1.1R+1.05S}=?\) --> \(\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}\). Now, as \(2R=3S\) then \(70R=105S\) (multiplying by 35) --> substitute 105S by 70R: \(\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}\)

Hope it's clear.


Yeah, I'm afraid I made the same mistake by using differentials we only find the ratio of votes for LAST YEAR, we are being asked something else.
Agree with method by Bunuel to solve this. I think more than one got caught with the 60%

Cheers!
J :)
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Re: Kumannia  [#permalink]

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New post 03 Jan 2014, 03:56
Hi Bunuel,
I have a clarification though...

After we get 2R = 3S as the equation for the total voters this year, doesn't this imply R/S = 3/2 and therefore R/(R+S) = 3/5? (After all, we derived 2R = 3S considering the voters increased 10% and 5% respectively this year?)

Appreciate any explanation.


Bunuel wrote:

Set the equation for the number of total voters this year: \(1.1R+1.05S=1.08(R+S)\) --> \(2R=3S\)

The question is \(\frac{1.1R}{1.1R+1.05S}=?\) --> \(\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}\). Now, as \(2R=3S\) then \(70R=105S\) (multiplying by 35) --> substitute 105S by 70R: \(\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}\)

Hope it's clear.
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Re: Kumannia  [#permalink]

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New post 03 Jan 2014, 04:10
mniyer wrote:
Hi Bunuel,
I have a clarification though...

After we get 2R = 3S as the equation for the total voters this year, doesn't this imply R/S = 3/2 and therefore R/(R+S) = 3/5? (After all, we derived 2R = 3S considering the voters increased 10% and 5% respectively this year?)

Appreciate any explanation.


Bunuel wrote:

Set the equation for the number of total voters this year: \(1.1R+1.05S=1.08(R+S)\) --> \(2R=3S\)

The question is \(\frac{1.1R}{1.1R+1.05S}=?\) --> \(\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}\). Now, as \(2R=3S\) then \(70R=105S\) (multiplying by 35) --> substitute 105S by 70R: \(\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}\)

Hope it's clear.


Yes, from \(2R=3S\) we get R/(R+S)=3/5, but notice that R and S there denote the number of voters last year.
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Last year, all registered voters in Kumannia voted either  [#permalink]

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New post 02 Dec 2015, 03:19
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mniyer wrote:
Hi Bunuel,
I have a clarification though...

After we get 2R = 3S as the equation for the total voters this year, doesn't this imply R/S = 3/2 and therefore R/(R+S) = 3/5? (After all, we derived 2R = 3S considering the voters increased 10% and 5% respectively this year?)

Appreciate any explanation.


Bunuel wrote:

Set the equation for the number of total voters this year: \(1.1R+1.05S=1.08(R+S)\) --> \(2R=3S\)

The question is \(\frac{1.1R}{1.1R+1.05S}=?\) --> \(\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}\). Now, as \(2R=3S\) then \(70R=105S\) (multiplying by 35) --> substitute 105S by 70R: \(\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}\)

Hope it's clear.


As Bunuel already stated R/Total = 3/5 is a ration for the last year, for this year yoiu must do the following:
Revolutionary voters: 3+10% Increase = \(3+\frac{3}{10}=\frac{33}{10}\)
Total: 5 + 8% Increase = 5+0,4 = \(\frac{54}{10}\)
So the fraction for this year is equal to \(\frac{33}{10}:\frac{54}{10}\) = \(\frac{33}{10}*\frac{10}{54}=\frac{11}{18}\)
Hopoe it's clear now
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Re: Last year, all registered voters in Kumannia voted either  [#permalink]

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New post 17 Apr 2016, 07:15
110X + 105Y = 108 (X+Y)
2X = 3Y

the question is:
110x/110x + 105y =?

if 2x = 3y => 70x = 105y when multiplied by 35.


then, 110x/(110x + 70x) = 110x/180x = 11/18
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Re: Last year, all registered voters in Kumannia voted either  [#permalink]

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