a) We have the votes for 55 people out of 80.
We have to find the minimum number of votes needed by Donahue to be sure that he will win the election.
There are 80 - 55 = 25 votes remaining.
Donahue has 24 votes already. The second candidate in number of votes has 18 votes, which is a difference of 6 votes.
We can think of a situation where the remaining votes are given to this two candidates and both have the same votes.
This would mean an amount of 24 + 18 + 25 = 67 votes.
Then, they won't have the same votes but we can think of Donahue having 67/2 = 33.5 ≈ 34 votes, and Garza having 33.
Then, this is the most extreme situation where Donahue wins by one vote.
We can then calculate the difference of votes he needs as 34 - 24 = 10 votes.
b) We can think again the same situation, but with Garza having 34 votes and Donahue having 33 votes.
This the extreme situation where Garza wins by the minimum difference.
Then, Garza would have to add 34 - 18 = 16 votes at least to win in this situation.
Answer:
a) Donahue needs 10 more votes to be sure he wins the election.
b) Garza needs at least 16 votes to be sure he wins the election.