Question

According to a poll, 56% of voters are likely to vote for the incumbent. The poll has a 3% margin of error. The margin of error means that the difference between the actual percent of voters and the percent determined by the poll is 3%. Write and solve an absolute value equation to find the least and the greatest percent of voters, x, likely to vote for the incumbent. a. The absolute value equation that represents this situation is

Answer 1

Answer:

a. ║x - p║ = 3% b. the least percent of voters for the incumbent is 53 % and the greatest percent of voters for the incumbent is 59 %

Step-by-step explanation:

a. Let x represent the number of voters and p represent the percentage determined by the poll. Since we have a 3 % margin error, we have

x - p = ± 3%.

So, ║x - p║ = 3%

b. So, we solve the equation to find the least and greates percent of incumbent likely to vote.

So, ║x - p║ = 3%

⇒ x - p = 3 % or - (x - p) = 3 %

Since p = 56 %,

x - p = 3%

x - 56 % = 3 %

x = 3% + 56 %

x = 59 %

Also -(x - p) = 3%

x - p = -3%

x - 56 % = -3%

x = 56 % - 3 %

x = 53 %

So, the least percent of voters for the incumbent is 53 % and the greatest percent of voters for the incumbent is 59 %