In a recent form captain election, Jono received 40 votes more than 40% of the votes. David received 10 votes more than 10% of the vote and Salah received 20 vo

Question

need help by like 30 mins.

full question:

In a recent form captain election, Jono received 40 votes more than 40% of the votes.
David received 10 votes more than 10% of the vote and Salah received 20 votes less than 20% of the vote. Damien received the remaining 180 votes.
How many votes were cast in the election and how many votes did each candidate get?

Answer 1

Assign variables to the values the problem asks us to find.

  Let x= How many votes were cast in the election

       J = number of Jono’s votes

       D = number of David’s votes

       S = number of Salah’s votes

       M = number of Damien’s votes

 

Now, translate:

  “Jono received 40 votes more than 40% of the votes”   means

      J             =             40           +                (40/100)*x

  “David received 10 votes more than 10% of the vote”   means

      D            =          10                    +         (10/100)*x

  “Salah received 20 votes less than 20% of the vote”   means

       S             =             -20                     (20/100)*x

  “Damien received the remaining 180 votes”   means

             M        =                                 180

 

The total number of votes:

    x  =    J                   +           D              +         S                +        M

    x = ( (40/100)x + 40 )  +  ( (10/100)x + 10)  +  ( (20/100)x  - 20 )  +  180

    100x = 40x + 4000 + 10x + 1000 + 20x -2000 + 18000   [multiply by 100 to get rid of fractions]

     30x  =  21000                                         [collect terms]

      x   =  700                                         [divide each side by 3]

 

      J = (40/100)(700)+40

      J = 320

 

      D = (10/100)(700) + 10

      D = 80

 

      S = (20/100)(700)-20

      S = 120

 

      M = 180

 

Checking (very important):

  Is    320 + 80 + 120 + 180  =  700  ?

             700 = 700   ? yes