Explanation Given: A small country consists of four states, A, B, and C. The population of each state is given as, State A B C Population 1 , 200 , 000 2 , 300 , 000 2 , 500 , 000 The given seats of legislature in the country are 76 . Approach: The formula for standard divisor is, d = Totatl population Total number of seats Here, d is standard divisor. The formula for standard quota, q = state's population d Here, q is standard quota. The lower quota is defined as standard quota of a state truncated to a whole number and upper quota is the standard quota of a state rounded up to next whole number. Calculation: Express each state’s population in thousands as follows, State A B C Population (thousands) 1 , 200 , 000 1000 = 1200 2 , 300 , 000 1000 = 2300 2 , 500 , 000 1000 = 2500 Table ( 1 ) Calculate the total population as follows, Total population = 1200 + 2300 + 2500 = 6000 Thousands The standard divisor is as follows, Substitute 76 for total number of seats and 6000 Thousands for total population in standard divisor formula, d = 6000 76 = 78.9474 ≈ 78.95 The standard quota for each state is as follows, For A: Substitute 1200 thousand for population of state and 78.95 for d in standard quota formula,

MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS

8th Edition

ISBN: 9780357537343

Author: Johnson

Publisher: CENGAGE L

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Chapter 6.CR, Problem 3CR

To determine

To apportion:

The legislative seats by using Hamilton’s method.

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MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS

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To apportion: The legislative seats by using Hamilton’s method.

Solution Summary: The author explains how to apportion the 76 legislative seats by using Hamilton's method.