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?

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 =

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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