942 CHAPTER 14 Voting and Apportionment Exercises Warm Up Exercises In Exercises 1–10, fill in the blank with an appropriate word, phrase, or symbol(s). 1. The total population under consideration divided by the number of items to be allocated is called the standard ________. Divisor 2. When each group’s population is divided by the standard divisor, a standard ________ is obtained. Quota 3. A standard quota rounded up to the nearest integer is called a(n) ________ quota. Upper 4. A standard quota rounded down to the nearest integer is called a(n) ________ quota. Lower 5. The rule stating that an apportionment should always be either the upper quota or the lower quota is called the ________ rule. Quota 6. Jefferson’s method, Webster’s method, and Adams’ method require using a(n) ________ quota. Modified 7. The apportionment method that requires rounding the standard quota down to the lower quota is called ________ method. Hamilton’s 8. a) The apportionment method that uses a modified divisor that is less than the standard divisor is ________ method. Jefferson’s b) The apportionment method that uses a modified divisor that is greater than the standard divisor is ________ method. Adams’ c) The apportionment method that uses a modified divisor that could be less than, greater than, or equal to the standard divisor is ________ method. Webster’s 9. a) The apportionment method that uses a modified quota that is always rounded to the nearest integer is ________ method. Webster’s b) The apportionment method that uses a modified quota that is always rounded up to the nearest integer is ________ method. Adams’ c) The apportionment method that uses a modified quota that is always rounded down to the nearest integer is ________ method. Jefferson’s 10. Jefferson’s method, Webster’s method, and Adams’ method all make use of a modified quota and can all lead to violations of the ________ rule. Quota Practice the Skills/Problem Solving In Exercises 11– 49, when appropriate round quotas to the nearest hundredth. Legislative Seats In Exercises 11–18, suppose that Sea Isle is a small country with a population of 7,500,000 that consists of four states, A,B C, , and D. There are 150 seats in the legislature that need to be apportioned among the four states. The population of each state is shown in the table below. State A B C D Total Population 1,220,000 2,730,000 857,000 2,693,000 7,500,000 11. a) Determine the standard divisor. 50,000 b) Determine each state’s standard quota. 24.40, 54.60, 17.14, 53.86 12. Determine each state’s apportionment using Hamilton’s method. 24, 55, 17, 54 13. a) Determine each state’s modified quota using the divisor 49,300. 24.75, 55.38, 17.38, 54.62 b) Determine each state’s apportionment using Jefferson’s method. 24, 55, 17, 54 14. a) Determine each state’s modified quota using the divisor 49,250. 24.77, 55.43, 17.40, 54.68 b) Determine each state’s apportionment using Jefferson’s method. 24, 55, 17, 54 15. Determine each state’s apportionment using Webster’s method using the standard divisor. 24, 55, 17, 54 16. a) Determine each state’s modified quota using the divisor 49,900. 24.45, 54.71, 17.17, 53.97 b) Determine each state’s apportionment using Webster’s method. 24, 55, 17, 54 17. a) Determine each state’s modified quota using the divisor 50,700. 24.06, 53.85, 16.90, 53.12 b) Determine each state’s apportionment using Adams’ method. 25, 54, 17, 54 18. a) Determine each state’s modified quota using the divisor 50,600. 24.11, 53.95, 16.94, 53.22 b) Determine each state’s apportionment using Adams’ method. 25, 54, 17, 54 Surf Boards In Exercises 19–26, a hotel chain in Hawaii needs to apportion 25 new surfboards for its visitors to rent among three hotels based on the numbers of rooms in each hotel as shown in the following table. SECTION 14.3 Hotel A B C Total Number of rooms 306 214 155 675
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