Question

Diane received the remaining 180 votes. How many votes were cast in the election and who was the
winner?

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

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

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