student election 584 students voted for 1 of 2 candidates. Winner received 122 more votes than loser how many votes were cast for each candidate
There are 584 students who will vote for two candidates.
Then the total votes for both candidates is 584 vote.
Given that the winner candidate received 122 more votes than the loser candidate.
Let the winner candidates recieves x votes.
Then, the loser candidate will receive x - 122.
==> x + ( x-122) = 584
==> 2x - 122 = 584
==> 2x = 706
=> x = 706/2 = 353
Then the winner received 353 votes.
The loser recieved 353-122 = 231 votes
We know that the total number of votes cast was 584. It is also known that the winner got 122 more votes than the loser.
Therefore is the loser received L number of votes, the winner got L+ 122 votes. As all students voted for either of the candidates L+L+122 = 584
=> 2L + 122 = 584
=> 2L = 584 - 122
=> 2L = 462
=> L = 231
So the loser get 231 votes and the winner gets 353 votes.
Let winner and loser get the votes x and y respectively.
The number votes by the winner is 122 more. So x = y+122.
The total votes polled is 584.
So x+y = 584. Put x= y+122 inthis equation and we get:
y+122+ y = 584.
2y +122 = 584.
2y = 584 -122 = 462
2y = 462
y = 462/2 = 231
Therefore x = 231+122 = 353.
So the winner gets 353 votes and the loser gets = 231 vote.