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 = 
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
