Question 78643
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+220}}}


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


{{{w+L=810}}}


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


{{{highlight(L+220)+L=810}}}


{{{2L+220=810}}} Now add like terms


{{{2L=590}}} Subtract 220 from both sides


{{{(2/2)L=590/2}}} 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+220}}}


{{{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+L=810}}} Plug in w=515,L=295
{{{515+295=810}}}
{{{810=810}}} works. So this verifies our answer.