Word Problem 8

Problem 8 : At an election where there are two candidates only. The candidate who gets 62 perecent of the votes is elected by majority of 144 votes. The total number of votes are;

a. 350           b. 500        c. 600              d. 1000

Discrete mathematics, finite mathematics —


Let us suppose;

Total votes =x

And let there be two candidates A & B

As per given data;

‘A’ gets 62 % of ‘x’ votes

i-e A's Votes= \frac{62}{100}x

So, remaining votes will then go to candidate ‘B’

i-e B's Votes=x- \frac{62}{100}x= \frac{38}{100}x

But ‘A’ wins by majority of 144 votes. Or we cans say that ‘A’ gets 144 votes more than ‘B’. So, if 144 votes are added to B’s votes then A’s and B’s votes will be equal;

i-e A's Votes = 144+B's Votes

\Rightarrow \frac{62}{100}x=144+\frac{38}{100}x

Simplification will give us


i-e total votes were 600