SOLUTION: 56. 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 ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: 56. 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 80391: 56. 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 erimir(14) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of votes received by the winning candidate be y, and let the number of votes received by the loosing candidate be x.
Now we have boil all the information down to two linear equations:
For the first, we know that the winning candidate (y) had 220 more votes than the loser (x). Hence, y=x%2B220.
For the second, we know that the total number of votes that were cast was 810. Assuming that the winner (y) and the loser (x) were the only recipients of all these votes, we know that x and y added must be 810. Hence, x%2By=810.
Now we have two equations:
(1) y=x%2B220
(2) x%2By=810
Substituting (1) into (2):
x%2By=810 (2)
x%2B%28x%2B220%29=810
x%2Bx%2B220=810
2x=810-220
2x=590
x=295
Now substituting the value of x in eq (2) back into (1):
y=x%2B220 (1)
y=295%2B220
y=515

From this we know that x=295 and y=515.