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:

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 \(x?\)

Image Credit: Simpsons Wikia.

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