SOLUTION: In an election with three candidates for mayor (A, B, and C), the initial vote count gave A 200 more votes than B, and 500 more votes than C. An error was found, and 1% of A's init

Question 980029: In an election with three candidates for mayor (A, B, and C), the initial vote count gave A 200 more votes than B, and 500 more votes than C. An error was found, and 1% of A's initial votes went to B, and 2% of A's initial votes went to C, such that B had 100 more votes than C. How many votes did each of the three candidates have in the FINAL count.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
C=x
B=x+300
A=x+500
1% of As votes is 0.01(x+500) or 5+0.01x
B becomes (x+300)+5+0.01x
C becomes x)+10+0.02x
A has been reduced to x+500-15-0.03x
B and C
1.01x+305 -100=1.02x+10
1.01x+205=1.02x +10
195=0.01x
multiply both sides by 100
19,500=x
Initial count:
A=20000
B=19800
C=19500
1% of A is 200 votes
2% is 400 votes
A had 19400 votes
B had 20000 votes
C had 19900 votes
That is the final result.
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