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Math Help - urgent plz help me in thissss tricky q

  1. #1
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    Exclamation urgent plz help me in thissss tricky q

    hiii

    can anybody help me???
    in an election contested by 2 candidates,one secured 37% and lost the election by a margin of 16640 votes. Find the number of votes polled and the votes secured by the defeated candidate

    help

    gautamm
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  2. #2
    Member Glaysher's Avatar
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    Candidate that lost got 37%
    Candidate that won got 63%

    Candidate lost by 16640

    This is the difference between the two candidates

    So 16640 votes is 63 - 37 = 26%

    16640/26 = 640 votes same as 1%

    From this can work out 100% for total votes and 37% for votes candidate that lost got
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  3. #3
    MHF Contributor
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    Quote Originally Posted by gautam93 View Post
    hiii

    can anybody help me???
    in an election contested by 2 candidates,one secured 37% and lost the election by a margin of 16640 votes. Find the number of votes polled and the votes secured by the defeated candidate

    help

    gautamm
    I always say that if you know what you are supposed to find in a word problem then you have solved 30 percent of the problem already. The last 70 percent is the solution---which is playing around or concentrating on how to get what you are asked to find. :-)

    In your word problem here, you are asked to find the total number of votes polled, and the votes secured by the defeated candidate.

    Easy. The problem is 30 percent solved already!

    You don't know yet those two so you assign variables or unknowns to them for now.
    Let V = total votes polled.
    And X = votes gathered by the defeated candidate.

    So you have two unknowns. You need two independent equations to solve for these two unknowns.

    The problem says the loser secured 37 percent of the total votes, so,
    X = 37% of V
    Or,
    X = (0.37)V -----Eq.(1)

    The problem also says the loser lost by a margin of 16,640 votes.
    That means the difference between the votes secured by the winner and the votes secured by the loser is 16,640 votes.
    If the loser got X votes, and the total votes is V, then the winner got (V-X) votes.
    So,
    (V-X) -X = 16,640
    V -2X = 16,640 -----Eq.(2)

    There, you have your two equations. Solved the problem!

    -------------
    Substitute the X from Eq.(1) into Eq.(2),
    V -2(0.37)V = 16,640
    V -(0.74)V = 16,640
    (0.26)V = 16,640
    V = (16,640)/(0.26) = 64,000 votes, total. -------answer.

    Plug that into Eq.(1),
    X = (0.37)(64,000) = 23,680 votes, secured by the loser. ----answer.

    Check:
    Votes of loser = 23,680 votes.
    So votes of winner = 64,000 -23,680 = 40,320 votes.
    Then,
    40,320 -23,680 =? 16,640
    16,640 =? 16,640
    Yes, so, OK.
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