SOLUTION: Social Science. Show the equation used for the solution. In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many vot

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Question 78643: Social Science. Show the equation used for the 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? Please help.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Let w=winner, L=loser
If the winner (w) had 220 more votes than the loser (L), then the winner's votes is equal to



Now if there were 810 votes total, then the winners votes and the losers votes would add to the total like this:



So we can substitute L+220 in for w like this



Now add like terms

Subtract 220 from both sides

Divide both sides by 2


So the loser had 295 votes. Since the winner had 220 more votes than the loser, we can add 220 to 295 to find out how many votes the winner had





So the winner had 515 votes while the loser had 295 votes


Check:
One way to check this is to add the winner's and the loser's votes together (we should get 810):

Plug in w=515,L=295

works. So this verifies our answer.
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