Question

how do you see it? the circle graph shows the results of a survey of registered voters the day of an election.
graph: which partys candidate will get your vote? other 4%, green 2%, libertarian 1%, democratic 47%, republican 42%. error: ±2%
the error given in the graph means that the actual percent could be 2% more or 2% less than the percent reported by the survey.

a. what are the minimum and maximum percents of voters who could vote republican? green?
the minimum percent of voters who could vote republican is □% and the maximum is □%. the minimum percent of voters who could vote green is □% and the maximum is □%.

b. how can you use absolute value equations to represent your answers in part (a)?

Explanation:

Part (a)

Republican Voters

Step1: Find minimum percent

The reported percent for Republican is 42%, and the error is ±2%. To find the minimum, subtract 2% from 42%.
$42 - 2 = 40$

Step2: Find maximum percent

To find the maximum, add 2% to 42%.
$42 + 2 = 44$

Green Voters

Step1: Find minimum percent

The reported percent for Green is 2%, and the error is ±2%. To find the minimum, subtract 2% from 2%.
$2 - 2 = 0$

Step2: Find maximum percent

To find the maximum, add 2% to 2%.
$2 + 2 = 4$

For a group with reported percent \( p \) and error \( e \) (here \( e = 2 \)), the actual percent \( x \) satisfies \( |x - p|=e \). For Republican (\( p = 42 \)), \( |x - 42| = 2 \). For Green (\( p = 2 \)), \( |x - 2| = 2 \). Solving these gives the min/max (e.g., \( x - 42 = \pm2 \) leads to \( x = 42\pm2 \), same for Green).

Answer:

(Part a):
The minimum percent of voters who could vote Republican is $\boldsymbol{40}$% and the maximum is $\boldsymbol{44}$%. The minimum percent of voters who could vote Green is $\boldsymbol{0}$% and the maximum is $\boldsymbol{4}$%.

Part (b)