Question

How to solve following question?

In an upcoming election, 15% of married voters will vote for Candidate A, while the rest will vote for Candidate B; 80% of unmarried voters will vote for Candidate A, while the rest will vote for Candidate B. Which of the following represents the lowest percentage from all voters combined (married and unmarried) that must be unmarried (not married) in order for Candidate A to win the election?

Answer 1

The lowest percentage from all voters combined that must be unmarried in order for Candidate A to win the election is 53.85%.

Explanation:

Proportion married:

x are married

1 - x are unmarried.

Will vote for candidate A:

15% of x

80% of 1 - x. So

`0.15x + 0.8(1-x)`

Candidate A wins:

If his proportion is more than 50%, that is:

`0.15x + 0.8(1-x) > 0.5`

`0.15x+ 0.8 - 0.8x > 0.5`

`-0.65x > -0.3`

`0.65x < 0.3`

`x < (0.3)/(0.65)`

`x < 0.4615`

Highest percentage of married is 46.15%, so:

The lowest percentage of unmarried is:

100 - 46.15 = 53.85%.

The lowest percentage from all voters combined that must be unmarried in order for Candidate A to win the election is 53.85%.