Question

How to solve following question?

Answer 1

Answer:

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

Step-by-step 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:

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

$0.15x+ 0.8 - 0.8x > 0.5$

$-0.65x > -0.3$

$0.65x < 0.3$

$x < \frac{0.3}{0.65}$

$x < 0.4615$

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%.