SOLUTION: Hi I wasn't sure how to set it up correctly. I've been trying but I'm not getting the correct answer. In a two-candidate election 1401 votes were cast. If 30 voters had switched th

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Question 779006: Hi I wasn't sure how to set it up correctly. I've been trying but I'm not getting the correct answer. In a two-candidate election 1401 votes were cast. If 30 voters had switched their votes from the winner to the loser, the loser would have won by 5 votes. How many votes did each candidate actually receive?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be votes for the winner
Then 1401-xis votes for the loser
So, we have
%28x-30%29%2B5=%281401-x%29%2B30....... simplify
x-25=1431-x.... add x and also 25 to both sides
x%2Bx-25%2B25=1431%2B25-x%2Bx...... collect like terms
2x=1456...... divide each side by 2
x=highlight%28728%29.....=> votes for the winner
1401-x=1401-728=+highlight%28673%29........=> votes for the loser