Question 916668: Hello!
in an election, 2.8 million votes were cast and each vote was for either Candidate 1 or Candidate 2. Candidate 2 received 28,000 more votes than Candidate 1. What percent of the 2.8 million votes were cast for Candidate 1?
thank you
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 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 = 49.5%
So Candidate 1 got 49.5% 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.
Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html
Thanks,
Jim
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