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13 Oct 2016, 12:21
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There were 5 candidates (Alexa, Bill, Charlie, Dan, and Ernie) vying for student council,
and 100 total votes were cast. Everyone received at least one vote, and no two
candidates received the same number of votes. Alexa won the election with 40 votes,
Bill came in 2nd, Charlie in 3rd, Dan in 4th, and Ernie in last.
1. What is the greatest number of votes that Bill could have received? What is the
least number?
2. What is the greatest number of votes that Charlie could have received? What is
the least number?
3. What is the greatest number of votes that Dan could have received? What is
the least number?
4. What is the greatest number of votes that Ernie could have received? What is
the least number?
5. If Bill received 25 votes, did Charlie get at least 13 votes?
6. If Charlie received 12 votes, did Dan get at least 5 votes?
Please assist with above problems.
and 100 total votes were cast. Everyone received at least one vote, and no two
candidates received the same number of votes. Alexa won the election with 40 votes,
Bill came in 2nd, Charlie in 3rd, Dan in 4th, and Ernie in last.
1. What is the greatest number of votes that Bill could have received? What is the
least number?
2. What is the greatest number of votes that Charlie could have received? What is
the least number?
3. What is the greatest number of votes that Dan could have received? What is
the least number?
4. What is the greatest number of votes that Ernie could have received? What is
the least number?
5. If Bill received 25 votes, did Charlie get at least 13 votes?
6. If Charlie received 12 votes, did Dan get at least 5 votes?
Please assist with above problems.
13 Oct 2016, 17:45
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There were 5 candidates (Alexa, Bill, Charlie, Dan, and Ernie) vying for student council,
and 100 total votes were cast. Everyone received at least one vote, and no two
candidates received the same number of votes. Alexa won the election with 40 votes,
Bill came in 2nd, Charlie in 3rd, Dan in 4th, and Ernie in last.
1. What is the greatest number of votes that Bill could have received? What is the
least number?
greatest - let other two be lowest possible but with B less than 40, so 39..
Lowest- let B,C,D,E get almost same so it would be 60/4=15..
But it is different so 13,14,16,17... ans 17
2. What is the greatest number of votes that Charlie could have received? What is
the least number?
greatest- C is one less than B and D and E get 1 and 2...so B + C = 60-1-2=57.... so B gets 29 and C 28...
Least- B gets 39 and rest three continuous integers.. so C+ D+E= 100-40-39=21....
So D gets 7, C-8 and E-6...ans 8
3. What is the greatest number of votes that Dan could have received? What is
the least number?
greatest is when E gets 1 and rest 3 gets continuous integers..
And lowest as shown above
4. What is the greatest number of votes that Ernie could have received? What is
the least number?
Similarly you can work out here
5. If Bill received 25 votes, did Charlie get at least 13 votes?
take worst case that C,D,and E get continuous integers..
So 100-40-25=35....10,12,13... so C has to get 13
6. If Charlie received 12 votes, did Dan get at least 5 votes?
same here worst case...
D and E get 100-40-39-12= 9.... so D and E in worst case scenario for D get 5 and 4...
So here too ans is YES
and 100 total votes were cast. Everyone received at least one vote, and no two
candidates received the same number of votes. Alexa won the election with 40 votes,
Bill came in 2nd, Charlie in 3rd, Dan in 4th, and Ernie in last.
1. What is the greatest number of votes that Bill could have received? What is the
least number?
greatest - let other two be lowest possible but with B less than 40, so 39..
Lowest- let B,C,D,E get almost same so it would be 60/4=15..
But it is different so 13,14,16,17... ans 17
2. What is the greatest number of votes that Charlie could have received? What is
the least number?
greatest- C is one less than B and D and E get 1 and 2...so B + C = 60-1-2=57.... so B gets 29 and C 28...
Least- B gets 39 and rest three continuous integers.. so C+ D+E= 100-40-39=21....
So D gets 7, C-8 and E-6...ans 8
3. What is the greatest number of votes that Dan could have received? What is
the least number?
greatest is when E gets 1 and rest 3 gets continuous integers..
And lowest as shown above
4. What is the greatest number of votes that Ernie could have received? What is
the least number?
Similarly you can work out here
5. If Bill received 25 votes, did Charlie get at least 13 votes?
take worst case that C,D,and E get continuous integers..
So 100-40-25=35....10,12,13... so C has to get 13
6. If Charlie received 12 votes, did Dan get at least 5 votes?
same here worst case...
D and E get 100-40-39-12= 9.... so D and E in worst case scenario for D get 5 and 4...
So here too ans is YES
03 Oct 2025, 04:54
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