SOLUTION: In a recent election Corrine Brown received 13,204 more votes than Bill Randall. If the total number of votes was ​119,548 find the number of votes for each candidate.

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Question 1173890: In a recent election Corrine Brown received 13,204 more votes than Bill Randall. If the total number of votes was ​119,548 find the number of votes for each candidate.
Found 2 solutions by mila nedic, ikleyn:
Answer by mila nedic(19)   (Show Source): You can put this solution on YOUR website!
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.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

There is short, quick and elegant way to solve it.


You write the system of two equations EXACTLY as you read the text


    Corrine - Bill =  13204    (1)

    Corrine + Bill = 119548    (2)


Then you add the equations


    2*Corrine = 13204 + 119548 = 132752

and divide by 2

      Corrine = 132752/2 = 66376.


Now from equation (2) you get

     Bill = 119548 - 66376 = 53172.


ANSWER.  Corrine 66376;   Bill 53172.

Solved.

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