Question 891431: In an election contested between A and B, A obtained votes equal to twice the no. Of persons on the electoral roll who didn't cast their votes and this later no. Was equal to twice his majority over B. If there were 18000 persons or the electoral roll how many voted for B
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! There are three categories:
Those who voted for A
Those who voted for B
Those who did not vote (we'll call this "C")
A = 2C [A obtained votes equal to twice the no. Of persons on the electoral roll who didn't cast their votes]
C = 2(A-B) [this later no. Was equal to twice his majority over B] C = 2A - 2B
A + B + C = 18,000
Substitute the value of C from the second equation into the first.
A = 2(2A-2B)
Distribute
A = 4A-4B
Add 4 B to each side
4B = 4A - A
4B = 3A
Divide each side by 4
B =  A [Let's change it to .75A for ease of use]
B = .75A
C = 2(A-B) or C = 2A - 1.5A (twice B)
C = .5A
Back to A + B + C = 18,000
A + .75A + .5A = 18,000
2.25A = 18,000
Divide each side by 2.25
A = 8000
If A is 8000, then B is .75*8000, or 6,000. C is half of A, so 4,000.
.
A wins the election. Unless, of course, it's being held in Chicago.
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