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?

Algebra ->  Coordinate Systems and Linear Equations -> 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?      Log On


   

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) About Me  (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

x%2By=810

Also, since "the winning candidate had 220 more votes than the loser", this means the second equation is x=y%2B220

So we have the system

x%2By=810
x=y%2B220



y%2B220%2By=810 Plug in x=y%2B220 into the first equation. In other words, replace each x with y%2B220. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.



2y%2B220=810 Combine like terms on the left side


2y=810-220Subtract 220 from both sides


2y=590 Combine like terms on the right side


y=%28590%29%2F%282%29 Divide both sides by 2 to isolate y



y=295 Divide




Now that we know that y=295, we can plug this into x=y%2B220 to find x



x=%28295%29%2B220 Substitute 295 for each y


x=515 Simplify


Answer:

So our answer is x=515 and y=295 which means that the winning candidate had 515 votes and the losing candidate had 295 votes