math assignment

Mathematics #2

Apportionment

1. A teacher wishes to distribute 10 identical pieces of candy among 4 students, based on how many pages of a book they read last month, using Hamilton's method. The table below lists the total number of pages read by each student.

Child	Pages
Zach	405
Aidan	280
Bill	555
Jordan	530

Answer the following questions. Give all answer to at least 4 decimal places as appropriate. Find the divisor:  Find the quota for Zach:  Find the initial apportionment for Zach: 

2. 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 19 tutors, determine how many tutors should be assigned to each subject using Hamilton's method.

Subject	Students Enrolled	Tutors to Assign
Math	330
English	280
Chemistry	130
Biology	55

3. The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift.  Apportion 12 salespeople using Hamilton's method given the information below.

Shift	Morning	Midday	Afternoon	Evening
Average number of customers	145	330	415	510
Salespeople to assign

4. Three people invest in a treasure dive, each investing the amount listed below.  The dive results in 35 gold coins.  Using Hamilton's method, apportion those coins to the investors based on their investment.

Investor	Investment	Allocation of 35 coins
Samantha	$18,350
Kendra	$12,290
Zoe	$4,360

  Right before the coins are distributed, the divers find one more coin they had misplaced.  Redo the allocation, now with 36 coins

Investor	Investment	Allocation of 36 coins
Samantha	$18,350
Kendra	$12,290
Zoe	$4,360

  Does this situation illustrate any apportionment issues?        

5. The legislature in a state has 39 seats.  Apportion these seats to the five counties below using Hamilton's method.

County	Population	Seats Received
Adams	274,000
Grant	385,000
Colton	307,000
Davis	431,000
Hayes	152,000

6. The legislature in a state has 35 seats.  Apportion these seats to the six counties below using Hamilton's method.

County	Population	Seats Received
Adams	300,000
Grant	333,000
Colton	227,000
Davis	305,000
Hayes	477,000
McKinley	80,000

7. A legislator in a state consists of 50 seats.  Apportion the seats to the counties using Hamilton's method.

County	Population	Seats
Jefferson	30,000
Clay	15,600
Madison	34,600
Jackson	40,800
Franklin	59,000

  Ten years, the populations are recounted.  Reapportion the 50 seats.

County	Population	Seats
Jefferson	30,000
Clay	15,600
Madison	36,200
Jackson	40,800
Franklin	59,200

  Does this situation illustrate any apportionment issues?        

8. A school district has two high schools. The district could only afford to hire 16 guidance counselors.  Determine how many counselors should be assigned to each school using Hamilton's method.

School	Students Enrolled	Counselors to Assign
Lowell	6306
Fairview	3288

  The next year, a new school is opened, with 3768 students.  Using the divisor from above, determine how many additional counselors should be hired for the new school:   counselors.

After hiring that many new counselors, the district recalculates the reapportion using Hamilton's method.  Determine the outcome.

School	Students Enrolled	Counselors to Assign
Lowell	6306
Fairview	3288
New School	3768

Does this situation illustrate any apportionment issues?        

9. 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 18 tutors, determine how many tutors should be assigned to each subject using Jefferson's method.

Subject	Students Enrolled	Tutors to Assign
Math	270
English	265
Chemistry	135
Biology	85

What modified divisor did you use?  

10. The legislature in a state has 103 seats.  Apportion these seats to the four counties below using Jefferson's method.

County	Population	Initial Allocation	Seats Received
Adams	33,400
Grant	108,500
Colton	10,700
Davis	12,200

Does this situation illustrate any apportionment issues?        

11. The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift.  Apportion 15 salespeople using Jefferson's method given the information below.

Shift	Morning	Midday	Afternoon	Evening
Average number of customers	85	320	405	545
Salespeople to assign

What modified divisor did you use?  

12. The legislature in a state has 30 seats.  Apportion these seats to the five counties below using Jefferson's method.

County	Population	Seats Received
Adams	106,000
Grant	425,000
Colton	432,000
Davis	405,000
Hayes	298,000

13. The legislature in a state has 36 seats.  Apportion these seats to the six counties below using Jefferson's method.

County	Population	Seats Received
Adams	213,000
Grant	449,000
Colton	407,000
Davis	241,000
Hayes	425,000
McKinley	460,000

14. A college offers tutoring in Math, English, Chemistry, and Biology. The number of students enrolled in each subject is listed below. The college can only afford to hire 20 tutors.  Use Webster's method to determine the initial allocations with the standard divisor, then finish the apportionment to determine how many tutors should be assigned to each subject.

Subject	Students Enrolled	Initial Allocation	Tutors to Assign
Math	355
English	265
Chemistry	110
Biology	60

What modified divisor did you use for the final apportionment?  

15. The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift.  Apportion 19 salespeople using Webster's method given the information below.

Shift	Morning	Midday	Afternoon	Evening
Average number of customers	135	275	370	450
Salespeople to assign

What modified divisor did you use?  

16. The legislature in a state has 44 seats.  Apportion these seats to the five counties below using Webster's method.

County	Population	Seats Received
Adams	147,000
Grant	192,000
Colton	492,000
Davis	183,000
Hayes	115,000

17. The legislature in a state has 59 seats.  Apportion these seats to the six counties below using Webster's method.

County	Population	Seats Received
Adams	79,000
Grant	400,000
Colton	180,000
Davis	178,000
Hayes	318,000
McKinley	330,000

18. A college offers tutoring in Math, English, Chemistry, and Biology. The number of students enrolled in each subject is listed below. The college can only afford to hire 13 tutors.  Using Huntington-Hill's method determine the initial geometric means and the initial allocations with the standard divisor.  You do not need to finish the apportionment.

Subject	Students Enrolled	Initial Geometric Mean	Initial Allocation
Math	290
English	230
Chemistry	130
Biology	70

Give decimal answers accurate to at least 3 decimal place

19. The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift.  Apportion 17 salespeople using Huntington-Hill's method given the information below.

Shift	Morning	Midday	Afternoon	Evening
Average number of customers	125	305	425	555
Salespeople to assign

What modified divisor did you use?  

20. The legislature in a state has 47 seats.  Apportion these seats to the five counties below using the Huntington-Hill method.

County	Population	Seats Received
Adams	466,000
Grant	238,000
Colton	218,000
Davis	259,000
Hayes	402,000

21. The legislature in a state has 53 seats.  Apportion these seats to the six counties below using the Huntington-Hill method.

County	Population	Seats Received
Adams	321,000
Grant	191,000
Colton	334,000
Davis	103,000
Hayes	130,000
McKinley	249,000

22. A college offers tutoring in Math, English, Chemistry, and Biology. The number of students enrolled in each subject is listed below. The college can only afford to hire 20 tutors.  Using Lowndes's method determine the decimal/whole ratios (to 4 decimal places) and the final apportionment. 

Subject	Students Enrolled	Ratios	Tutors assigned
Math	260
English	260
Chemistry	155
Biology	85

23. The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift.  Apportion 22 salespeople using Lowndes' method given the information below.

Shift	Morning	Midday	Afternoon	Evening
Average number of customers	100	280	380	560
Salespeople to assign

24. The legislature in a state has 45 seats.  Apportion these seats to the five counties below using Lowndes' method.

County	Population	Seats Received
Adams	248,000
Grant	305,000
Colton	185,000
Davis	273,000
Hayes	395,000

25. The legislature in a state has 56 seats.  Apportion these seats to the six counties below using Lowndes' method.

County	Population	Seats Received
Adams	469,000
Grant	176,000
Colton	186,000
Davis	177,000
Hayes	190,000
McKinley	217,000