SOLUTION: PERCENTAGE QUESTION :- THERE WERE 2 CANDIDATES IN AN ELECTION. 10 % OF THE MEMBERS IN THE VOTER LIST DID NOT CAST VOTES. 60 VOTES WERE DECLARED INVALID. WINNING CANDIDATE SECUR

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: PERCENTAGE QUESTION :- THERE WERE 2 CANDIDATES IN AN ELECTION. 10 % OF THE MEMBERS IN THE VOTER LIST DID NOT CAST VOTES. 60 VOTES WERE DECLARED INVALID. WINNING CANDIDATE SECUR      Log On


   

Question 935212: PERCENTAGE QUESTION :-
THERE WERE 2 CANDIDATES IN AN ELECTION.
10 % OF THE MEMBERS IN THE VOTER LIST DID NOT CAST VOTES.
60 VOTES WERE DECLARED INVALID.
WINNING CANDIDATE SECURED 308 VOTES MORE THAN LOSING CANDIDATE.
IF 47% OF THE TOTAL MEMBER VOTED IN FAVOUR OF WINNING CANDIDATE.
FIND VOTE SECURED BY EACH CANDIDATE ??????
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
PERCENTAGE QUESTION :-
THERE WERE 2 CANDIDATES IN AN ELECTION.
Suppose there were N members in the voter list.
Suppose W votes were in favor of the winner.
Suppose L votes were in favor of the loser.

So 90% of N or 0.90N cast votes

60 VOTES WERE DECLARED INVALID.

So 0.90N-60 votes were valid

WINNING CANDIDATE SECURED 308 VOTES MORE THAN LOSING CANDIDATE.
W = L + 308
W + L = 0.90N-60

IF 47% OF THE TOTAL MEMBER VOTED IN FAVOUR OF WINNING CANDIDATE.
W = .47N

FIND VOTE SECURED BY EACH CANDIDATE ??????
We have 3 equations

W = L + 308
W + L = 0.90N-60
W = .47N

Substitute .47N in the first two:

.47N = L + 308
.47N + L = 0.90N-60

Multiple each through by 100

47N = 100L + 30800
47N + 100L = 90N-6000

 47N - 100L = 30800
-43N + 100L = -6000
-------------------
  4N        = 24800
   N        =  6200 

W = .47N
W = .47(6200)
W = 2914

W = L + 308
2914 = L + 308
2606 = L

Edwin