MA 125 - In-Class Assignment 1 - Spring 2008
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1. Five hundred students at a university are voting for a new school mascot. After 300 votes
have been counted, the tallies are as follows.
Purple People Eaters 106
Flying Squirrels 98
Rambling Platypi 96
(a) What is the minimum number of the remaining votes needed to guarantee that the new
mascot will be the Purple People Eaters? Explain.
The closest competitor is Flying Squirrels. To tie, Flying Squirrels would need 8 votes,
leaving 200 8 = 192 votes remaining. Purple People Eaters would need a majority of
these votes. Since 192 2 = 96;Purple People Eaters would need 97 of the remaining
votes to guarantee victory.
(b) What is the minimum number of the remaining votes needed to guarantee that the new
mascot will be the Flying Squirrels? Explain.
To tie Purple People Eaters, Flying Squirrels would need 8 votes, leaving 200 8 = 192
votes remaining. Flying Squirrels would need a majority of these votes. Since 192 2 =
96;Flying Squirrels would need 97 of these remaining votes, plus the additional 8 to tie,
to guarantee victory. So, Flying Squirrels would need 97 + 8 = 105 votes.
(c) What is the minimum number of the remaining votes needed to guarantee that the new
mascot will be the Rambling Platypi? Explain.
To tie Purple People Eaters, Rambling Platypi would need 10 votes, leaving 200 10 =
190 votes remaining. Flying Squirrels would need a majority of these votes. Since
1902 = 95;Flying Squirrels would need 96 of these remaining votes, plus the additional
10 to tie, to guarantee victory. So, Flying Squirrels would need 96 + 10 = 106 votes.
2. Suppose there were 15,364 votes an election involving six candidates.
(a) If a candidate is required to have majority of the votes cast to be considered the winner,
what is the minimum number of votes needed to win? Explain.
A majority win requires a vote tally over 50%. Fifty percent of 15;364 is 15364 :5 =
7682:So, a candidate would need 7683 votes to have over 50% and thus have a majority.
(b) If a candidate is needs a plurality of the votes cast to be considered the winner, what is
the minimum number of votes a winning candidate can have and still win the election?
Explain.
Dividing the votes equally among the candidates, we have 15364 6 = 2560:67:So,
each candidate could get 2560 votes, leaving four remaining votes. One extra vote for
a candidate will not gain that candidate victory as the remaining three votes must go
elsewhere, giving another candidate a total of at least 2561. So, a candidate must have
an addition two of the four votes, or 2562, in order to win. (This does not guarantee
victory, however.)
3. A university has 75 faculty members, and they need to vote for a faculty representative to the
Board of Trustees. There are four candidates running for this position, and the preference
