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05 Aug 2003, 14:01
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There will be problems that will require you really know how to manipulate algebra. Don't make the mistake I did and rely on picking numbers like I did for the SAT.
:!: :!: :!:
When 2/9 of the certain votes have been counted, 3/4 of those counted are in favor of the resolution. What fraction of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?
This is extremely challenging not to pick in numbers.
Victor
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When 2/9 of the certain votes have been counted, 3/4 of those counted are in favor of the resolution. What fraction of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?
This is extremely challenging not to pick in numbers.
Victor
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05 Aug 2003, 14:13
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11/14
Let the total # of voters be 36x
Already counted = 36x * 2/9 = 8x
Out of which,
For the resolution = 8x*3/4 = 6x
So, already counted and against = 8x-6x=2x
Counting left for 36x - 8x = 28x votes
Let, the "for" candidate gets y votes out of the 28x
So, "against" gets 28x-y
"For" gets in total = 6x+y
"Against" gets = 2x+28x-y=30x-y
Given, (30x-y)/(6x+y)=2
=> y=6x
So, the "against" party has to get 28x-y=28x-6x=22x out of the remaining 28x votes. So, ratio = 22/28 = 11/14
Let the total # of voters be 36x
Already counted = 36x * 2/9 = 8x
Out of which,
For the resolution = 8x*3/4 = 6x
So, already counted and against = 8x-6x=2x
Counting left for 36x - 8x = 28x votes
Let, the "for" candidate gets y votes out of the 28x
So, "against" gets 28x-y
"For" gets in total = 6x+y
"Against" gets = 2x+28x-y=30x-y
Given, (30x-y)/(6x+y)=2
=> y=6x
So, the "against" party has to get 28x-y=28x-6x=22x out of the remaining 28x votes. So, ratio = 22/28 = 11/14
05 Aug 2003, 15:51
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I find it easier to do it the other way;
3 + x
------- = 1/2
1 + 14 -x
I don't know what "X" stands for your in your problem. Mine is votes.
VT
3 + x
------- = 1/2
1 + 14 -x
I don't know what "X" stands for your in your problem. Mine is votes.
VT
