Answer
Winner $=1480$ votes.
Loser $=1320$ votes.
Work Step by Step
Let the votes cast for winner be $x$.
and the votes cast for loser be $y$.
Total votes $x+y=2800$......(1)
And because the number of votes for the winner were $160$ more than those for the loser, we have
$x=y+160$......(2)
Substitute the value of $x$ from equation (2) to equation (1).
$y+160+y=2800$
Add like terms and subtract $160$ from both sides.
$2y+160-160=2800-160$
$2y=2640$
Divide both sides by $2$.
$\frac{2y}{2}=\frac{2640}{2}$
Simplify.
$y=1320$
Plug the value of $y$ into equation (2).
$x=1320+160$
Simplify.
$x=1480$.
