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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-> 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.
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.
