SOLUTION: In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate receive?

Question 87271: In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate receive?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let w=# of votes for winning candidate, L=# of votes for losing candidate

Since the total of votes cast was 810 (ie the sum of both candidates votes), we get the equation

Since the winning candidate had 220 more votes than the losing candidate, this means that we simply add 220 to L to find w like this

For instance, lets say the losing candidate had 2 votes, then the winning candidate would have votes

Since , we can replace the w of the equation

Plug in

Combine like terms

Subtract 220 from both sides

Combine like terms on the right side

Divide both sides by 2

So we get

This means the losing candidate had 295 votes. To find out how many the winning candidate received, lets plug in into the other equation:

Plug in

Subtract 295 from both sides

So the winning candidate received 515 votes and the losing received had 295 votes.

Check:
Plug in and

works
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