Question 916668
x = # of votes for candidate 1 (this number is in millions)
y = # of votes for candidate 2 (this number is in millions)



First equation: 


x+y = 2.8


since a total of "2.8 million votes were cast and each vote was for either Candidate 1 or Candidate 2"


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28,000 = 28,000/1,000,000 = 0.028 million


Second equation:


y = x + 0.028


because "Candidate 2 received 28,000 more votes than Candidate 1"


this is the same as saying "Candidate 2 received 0.028 million more votes than Candidate 1"


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We'll use substitution to solve for x.



x+y = 2.8


x+x + 0.028 = 2.8 ... replace y with x + 0.028


2x+0.028 = 2.8


2x = 2.8-0.028


2x = 2.772


x = 2.772/2


x = 1.386



Remember that x =  # of votes for candidate 1 (this number is in millions)


Since x = 1.386, this means that Candidate 1 got 1.386 million votes.


Divide this by 2.8 (the total): 1.386/2.8 = 0.495


Multiply by 100: 0.495*100 = <font size=5 color="red">49.5%</font>


So Candidate 1 got <font size=5 color="red">49.5%</font> of the vote. 


Candidate 2 got 100 - 49.5 = 50.5% of the vote. This means Candidate 2 is the winner. This part can be easily determined from the fact that "Candidate 2 received 28,000 more votes than Candidate 1". Despite this, it helps to see the percentages as well.



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Thanks,


Jim