Question

in a two-candidate election 1401 votes were cast. if 30 voters had switched their votes from the winner to the loser, the loser would have won by 5 votes. How many votes did each candidate actually receive?

Answer 1

let x be the votes won by candidate A
y be the votes won by candidate B

total votes is 1401 so

x + y = 1401

if 30 votes switched from winner to loser then the winner would have won by 5 votes

let's say x won and y lost

so x - 30 = y+ 35 because x lost 30 votes and they go to y then why wins by 5 votes.

i can rewrite this as x - y = -5 if i subtract y from both sides and add 30 to both sides

now let's do the system

x + y = 1401
x - y = -5

add them

2x = 1396

divide both sides by 2

x = 698

so y has 703

this would be the one with the edited votes...to get the original just add 30 to x and subtract 30 from y so

x = 728
y = 673

Answer 2

does that help?

Answer 3

is there a way to write that into 1 equation