In a recent student body election, Adam received 40 more than 40% of the votes. Brigitte received 40 less than 50% of the number Adam receiv

Question

In a recent student body election, Adam received 40 more than 40% of the votes. Brigitte received 40 less than 50% of the number Adam received. Carl received 20 more than 50% of what Brigitte received, and
Diane received the remaining 180 votes. How many votes were cast in the election and who was the
winner?

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Charlie 6 days 2021-09-12T08:31:19+00:00 1 Answer 0

Answers ( )

    0
    2021-09-12T08:33:07+00:00

    Answer:

    The total number of vote cast is 700

    The maximum vote is of Adam, so He is winner  

    Step-by-step explanation:

    Given as :

    Let The total vote cast = v

    The vote received by Adam = A = 40 + 40 % of v

    I.e A = 40 + 0.4 × v                          …………..1

    The vote received by Brigitte = B = 50 % of A – 40

    I.e B = 0.5 × A – 40          

    or, B = 0.5 × ( 40 + 0.4 × v ) – 40

    Or, B = 20 + 0.2 v – 40

    ∴   B = 0.2 v – 20                      ……..2

    The vote received by Carl = C = 20 + 50 % of B

    I.e C = 20 + 0.5 × ( 0.2 v – 20 )

    or, C = 20 + 0.1 v – 10  

     C = 10 + 0.1 v              ………..3

    The vote received by Diane = D =  180 votes

    Now, According to question

    The total vote cast = The vote received by Adam + The vote received by Brigitte + The vote received by Carl + The vote received by Diane

    I.e v = A + B + C + D

    Or, v = (40 + 0.4 v) + (0.2 v – 20) + (10 + 0.1 v) + 180

    Or, v = (40 – 20 + 10 + 180) + ( 0.4 v + 0.2 v + 0.1 v )

    Or, v = 210 + 0.7 v

    Or . v – 0.7 v = 210

    Or 0.3 v = 210

    ∴ v = \frac{210}{0.3}

    I.e v = 700

    So, Total number of vote cast = v = 700

    Now, put the value of v in each equation

    So ,  A = 40 + 0.4 × v = 40 + 0.4 × 700 = 320

           B = 0.2 × v – 20 =  0.2 × 700 – 20 = 120

          C = 10 + 0.25 × v = 10 + 0.1  × 700 = 80

    So. Adam vote = 320

    Brigitte vote = 120

    Carl vote = 80

    Diane vote = 180

    So maximum vote is of Adam, so He is winner

    Hence The total number of vote cast is 700

    And The maximum vote is of Adam, so He is winner  Answer

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