Question 87271
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


{{{w+L=810}}}


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


{{{w=220+L}}}


For instance, lets say the losing candidate had 2 votes, then the winning candidate would have {{{220+2=222}}} votes


Since {{{w=220+L}}}, we can replace the w of the equation {{{w+L=810}}}


{{{highlight(220+L)+L=810}}} Plug in {{{w=220+L}}}


{{{220+2L=810}}} Combine like terms


{{{cross(220-220)+2L=810-220}}} Subtract 220 from both sides


{{{2L=590}}} Combine like terms on the right side


{{{L=590/2}}} Divide both sides by 2


So we get 

{{{L=295}}}

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


{{{w+highlight(295)=810}}} Plug in {{{L=295}}}


{{{w+cross(295-295)=810-295}}} Subtract 295 from both sides


{{{w=515}}}


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


Check:

{{{515+295=810}}} Plug in {{{w=515}}} and {{{L=295}}}


{{{810=810}}} works