SOLUTION: I have been struggling on this problem for awhile now and I was wondering if someone would help me? Please and Thank you!! I would deeply appreciate it! In a two-candidate elect

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Question 154576This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been struggling on this problem for awhile now and I was wondering if someone would help me? Please and Thank you!! I would deeply appreciate it!
In a two-candidate election 1401 votes were cast. If 30 voters had switched their votes from the winner to the loser, the loser would have won by 5 votes. How many votes did each candidate actually recieve? This question is from textbook Algebra and Trigonometry Structure and Method book 2

Found 3 solutions by Edwin McCravy, scott8148, stanbon:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
have been struggling on this problem for awhile now and I was wondering if someone would help me? Please and Thank you!! I would deeply appreciate it!
In a two-candidate election 1401 votes were cast. If 30 voters had switched their votes from the winner to the loser, the loser would have won by 5 votes. How many votes did each candidate actually recieve?

W = number of votes the winner received
L = number of votes the loser received.


>>...1401 votes were cast...<<

That means  W + L = 1401

>>...If 30 voters had switched their votes from
 the winner to the loser...<<

That means the winner would have gotten W-30 

and the loser would have gotten L+30 

>>...the loser would have won by 5 votes...<<

L+30 is 5 more than W-30 or

(L+30) = (W-30) + 5


So we have this system of equations:

system%28W%2BL=1401%2C%28L%2B30%29=%28W-30%29%2B5%29

Can you solve that system by simplifying the
second equation and then using substitution
or elimination?  If not post again asking how.

Answer: W = 728 votes, L = 673 votes.

They do add to 1401.

If the winner had had 30 votes less he would have had 698 votes.
If the loser had had 30 votes more he would have had 703 votes.
So the loser would have won by 5 votes.
So we have the right answer.  Just solve the system.

Edwin

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"In a two-candidate election 1401 votes were cast" __ W+L=1401 __ L=1401-W

"If 30 voters had switched their votes from the winner to the loser, the loser would have won by 5 votes"
__ (W-30)+5=(L+30)

substituting __ W-30+5=1401-W+30 __ adding W+25 __ 2W=1456 __ dividing by 2 __ W=728

substituting __ L=1401-W __ L=673

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
In a two-candidate election 1401 votes were cast.
Let the winner have x votes; let the loser have 1401-x votes
-------------------------------------------------------------
If 30 voters had switched their votes from the winner to the loser, the loser would have won by 5 votes.
winner = x -30
loser = 1401-x+30 = 1431-x
-----------------------------------
EQUATION:
loser - winner = 5 votes
1431-x - (x-30) = 5
1431 - x - x + 30 = 5
2x = 1461-5
2x = 1456
x = 728 votes
---------------------
How many votes did each candidate actually receive?
Winner had x = 728
Loser had 1401-x = 673 votes
==============================
Cheers,
Stan H.
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