Question

miss kelley is deciding what color to paint her classroom. she asks her students to vote for their first, second, and third choices. the results are in the table. using the ranked - choice method, which color would she eliminate first? after eliminating that color, which color has the most first - place votes and wins? a. she should eliminate green. yellow wins b. she should eliminate blue. yellow wins c. she should eliminate blue. green wins

Explanation:

Step1: Calculate the total first - place votes for each color

• Blue: \(7 + 21=28\)
• Green: \(11 + 20 = 31\)
• Yellow: \(18+13 = 31\)

Step2: Eliminate the color with the fewest first - place votes

Since Blue has the fewest first - place votes (\(28\)), it is eliminated first.

Step3: Redistribute the votes of the eliminated color

After eliminating Blue, we consider the second - place votes of the Blue voters.

• For the \(7\) voters who had Blue as first - choice: their second - choice is Green.
• For the \(21\) voters who had Blue as first - choice: their second - choice is Yellow.

Now, calculate the new first - place votes (excluding Blue)

• Green: \(11 + 20+7=38\)
• Yellow: \(18 + 13+21=52\)

Answer:

B. She should eliminate blue. Yellow wins