Question 1173890
Let's say Corrine's votes are represented by c and Bill's votes are represented by b. We can use these variable to create equations using the information we have.

Corrine received 13204 more votes than Bill: c=13204+b
The total number of votes was ​119548: c+b=119548

Since we know that c=13204+b, we can replace c with 13204+c in the second equation so we are only dealing with one variable:
c+b=119548
(13204+b)+b=119548
2b=106344
b=53172 (Bill had 53172 votes)
Now we can use one on the first equations to solve for Corrine)

c=13204+b
c=13204+53172
c=66376 (Corrine had 66381 votes)

Checking by using the other equation:
c+b=119548
53172+66376=119548 (since it adds up to 119548 we know it's correct)

Therefore Corrine had 66376 votes and Bill had 53172 votes.