SOLUTION: A college is trying to determine a nickname for its sports teams, and 4 different nicknames have been proposed. 4,783 people are all going to vote, and the nickname that receiv

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Question 1203470: A college is trying to determine a nickname for its sports
teams, and 4 different nicknames have been proposed.
4,783 people are all going to vote, and the nickname that
receives the highest number of votes will win.
What is the smallest number of votes that a nickname could
receive and be declared the winner?
What I did was divide 4783/4 and I got 1195.75 and I rounded up so therefore it is 1196. My teacher has the correct answer listed as 1197. What did I do wrong?
Found 3 solutions by MathLover1, ikleyn, greenestamps:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

you got , and that is the smallest number of votes that each nickname could receive
to win, one nickname should get, at least more vote than other two nicknames
so, the smallest number of votes that a nickname could receive and be declared the winner is
Answer by ikleyn(52767)   (Show Source): You can put this solution on YOUR website!
.
A college is trying to determine a nickname for its sports
teams, and 4 different nicknames have been proposed.
4,783 people are all going to vote, and the nickname that
receives the highest number of votes will win.
What is the smallest number of votes that a nickname could
receive and be declared the winner?
What I did was divide 4783/4 and I got 1195.75 and I rounded up so therefore it is 1196.
My teacher has the correct answer listed as 1197. What did I do wrong?
~~~~~~~~~~~~~~~~~~~


                                Good problem,  I  like it.
                        And good question,  I  like it,  too. 


Your idea to divide 4783 by 4 was right, but the remaining part of reasoning requires more accuracy.


Let's divide the number 4780 by 4: 4780/4 = 1195.


It tells us that if we distribute the votes in 4 boxes uniformly, we can put about 1195 votes in each of 4 boxes.


So, now our task is to distribute 3 remaining votes among 4 boxes in order for to get
the winning situation with a UNIQUE winner.


It requires to put the remaining 3 votes in this configuration  (2, 1, 0, 0) or in this (3, 0, 0, 0),
placing at least 2 votes in one box in order for a winner be UNIQUE.


It gives the number 1197 as the minimal required number of votes.

Is this reasoning totally clear to you ?



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


You divided the total of 4783 by 4 and got 1195.75, or 1195 3/4.

The "3/4" tells you that, for the votes to be distributed as evenly as possible, the votes for the four nicknames would be 1196, 1196, 1196, and 1195.

But that distribution of the votes does not produce a winner.

So the smallest number of votes that will produce a winner is 1197.
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