Apportionment
Dividing a fixed number of House seats among states by Hamilton's, Jefferson's, Webster's and Hill-Huntington methods, and the history that shaped them.
20 exercises
Exercise 1
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
A college offers tutoring in Math, English, Chemistry, and Biology. The number of students enrolled in each subject is listed below. If the college can only afford to hire 15 tutors, determine how many tutors should be assigned to each subject.
Exercise 2
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
Reapportion the previous problem if the college can hire 20 tutors.
Exercise 3
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift. Apportion 20 salespeople given the information below.
Exercise 4
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
Reapportion the previous problem if the store has 25 salespeople.
Exercise 5
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
Three people invest in a treasure dive, each investing the amount listed below. The dive results in 36 gold coins. Apportion those coins to the investor.
Exercise 6
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
Reapportion the previous problem if 37 gold coins are recovered.
Exercise 7
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
A small country consists of four states, whose populations are listed below. If the legislature has 116 seats, apportion the seats.
Exercise 8
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
Reapportion the previous problem with 124 seats.
Exercise 9
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
A small country consists of five states, whose populations are listed below. If the legislature has 119 seats, apportion the seats.
Exercise 10
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
Reapportion the previous problem with 126 seats.
Exercise 11
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
A small country consists of six states, whose populations are listed below. If the legislature has 200 seats, apportion the seats.
Exercise 12
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
Reapportion the previous problem with 180 seats
Exercise 13
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
A small country consists of six states, whose populations are listed below. If the legislature has 250 seats, apportion the seats.
Exercise 14
In exercises 1-14, determine the apportionment using
Hamilton's Method
Jefferson's Method
Webster's Method
Huntington-Hill Method
Reapportion the previous problem with 240 seats.
Exercise 15
A small country consists of three states, whose populations are listed below.
If the legislature has 10 seats, use Hamilton's method to apportion the seats.
If the legislature grows to 11 seats, use Hamilton's method to apportion the seats.
Explain what happened in part b. What do you think would be a fair solution?
Try Jefferson's method for 11 seats. Does that solve the problem?
Exercise 16
A small country consists of three states, whose populations are listed below.
If the legislature has 10 seats, use Hamilton's method to apportion the seats. Which rule is not met in this case?
If the legislature grows to 11 seats, use Hamilton's method to apportion the seats.
If there could only be 10 seats, what do you think would be a fair solution?
Exercise 17
A state with five counties has 50 seats in their legislature. Using Hamilton's method, apportion the seats based on the 2010 census, then again using the 2020 census. Explain what happened in 2020 apportionment. Do you think it is fair?
Exercise 18
A state with five counties has 62 seats in their legislature. Using Hamilton's method, apportion the seats based on the 2010 census, then again using the 2010 census. Explain what happened in 2020 apportionment. Do you think it is fair?
Exercise 19
A school district has two high schools: Clatsop, serving 1715 students, and Siletz, serving 7364. The district could only afford to hire 13 guidance counselors.
Determine how many counselors should be assigned to each school using Hamilton's method.
The following year, the district expands to include a third school, Cayuse, serving an additional 2989 students. Based on the divisor from above, how ma…
Exercise 20
A school district has two middle schools: Tubman, serving 451 students, and Blackshear, serving 176. The district could afford to hire 8 art teachers.
Determine how many art teachers should be assigned to each school using Hamilton's method.
The following year, the district expands to include a third school, Banneker, serving 231 additional students. Based on the divisor from above, how many additio…
Adapted from Math in Society © 2018–2024 Portland Community College Math Instructors. Licensed under CC BY-SA 4.0. Source: Math in Society. Imported at revision 68ee43c.