SOLUTION: 13. Social science. 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?
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Question 123629: 13. Social science. 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 x= # of votes for winning candidate, y=# of votes for losing candidate
Because, there were 810 votes in all, this means that the sum of the votes is 810. So the first equation is
Also, since "the winning candidate had 220 more votes than the loser", this means the second equation is
So we have the system
Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
Combine like terms on the left side
Subtract 220 from both sides
Combine like terms on the right side
Divide both sides by 2 to isolate y
Divide
Now that we know that , we can plug this into to find
Substitute for each
Simplify
Answer:
So our answer is and which means that the winning candidate had 515 votes and the losing candidate had 295 votes
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