Gerrymandering

Logic Level 2

In a recent election, Sideshow Bob and Joe Quimby decided to run for election for Mayor of Springfield. The decision depends on the results in two districts: City and Countryside. Whichever candidate wins both districts wins the election.

The results shows that

In the City: 15000 out of 25000 voted for Sideshow Bob, while 4000 out of 5000 voted for Joe Quimby.

In the Countryside: 1000 out of 5000 voted for Sideshow Bob, while 7500 out of 25000 voted for Joe Quimby.

Tabulation of data:

Candidate	City	Countryside
Sideshow Bob	\(\frac{15000}{25000} = 60\%\)	\(\frac{1000}{5000} = 20\%\)
Joe Quimby	\(\frac{4000}{5000} = \color{red}{\mathbf{80\%}}\)	\(\frac{7500}{25000} = \color{red}{\mathbf{30\%}}\)

Because there's a higher percentage of people who have voted for Joe Quimby in both the City and Countryside, Joe Quimby was re-elected as the Mayor of Springfield.

If the decision does not depend on winning individual districts, but instead on the winning more votes in the entire population, then show that Sideshow Bob would have won the election. Also, if Sideshow Bob beat Joe Quimby by \(x \% \) of the total voters, what is the value of \(x?\)

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.