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

Algebra ->  Linear-equations -> 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      Log On


   

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) About Me  (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

w=L%2B220

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

w%2BL=810

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

highlight%28L%2B220%29%2BL=810

2L%2B220=810 Now add like terms

2L=590 Subtract 220 from both sides

%282%2F2%29L=590%2F2 Divide both sides by 2

L=295
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

w=295%2B220

w=515

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):

w%2BL=810 Plug in w=515,L=295
515%2B295=810
810=810 works. So this verifies our answer.