First, calculate the total number of votes
[tex]151271+113122+47531+40856+13053=365833[/tex]
Then, the majority of the votes is
[tex]\frac{365833}{2}=182916.5\approx182917[/tex]
a) At least 182917 votes are needed to get a majority in the Electoral College.
Crawford's votes plus miscellaneous are equal to 53909.
Add them to Jackson's, Adam's, and Clay's to check whether they get a majority that way
[tex]\begin{gathered} 151271+53909=205180\ge182917 \\ 113122+53909=167031<182917 \\ 47531+53909=101440<182917 \end{gathered}[/tex]
Therefore, only Jackson could have won a majority of the votes.
b)
Calculate the number of extra votes Jackson needs to get a majority
[tex]182917-151271=31646[/tex]
Then, calculate the percentage that 31646 represents if 182917 is 100%.
[tex]\begin{gathered} \frac{x}{31646}=\frac{100}{182917} \\ \Rightarrow x\approx17.301 \end{gathered}[/tex]
Thus, Jackson needs 17.3% of the votes.
