Explanation Given: M = 3 , p A and p B denote the populations of A and B , respectively and the apportionment under Webster's method gives all three seats to A and none to B . Formula used: The modified quota is given as, Modified quota = state population D Here, the modified divisor is D . Calculation: Since, all three seats are given to A . Hence, modified quota for A lies between 2.5 and 3.5. Thus, 3.5 > p A D ≥ 2.5 Further solving, 3.5 D > p A ≥ 2.5 D ...... ( 1 ) Since no seat is given to B . Hence, p B D < 0.5 Further solving, p B < 0.5 D ...... ( 2 ) Multiply inequality (1) by 2. 7 D > 2 p A ≥ 5 D ...... ( 3 ) Multiply inequality (2) by 2. 2 p B < D .

Excursions in Modern Mathematics (9th Edition)

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ISBN: 9780134468372

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Publisher: PEARSON

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More than 8313% of the country’s population must live in state A.

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More than 83 1 3 % of the country’s population must live in state A .

Solution Summary: The author explains how Webster's method gives all three seats to A and none to B. The modified quota for A lies between 2.5 and 3.5.

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More than 8313% of the country’s population must live in state A.

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More than 83 1 3 % of the country’s population must live in state A .

Solution Summary: The author explains how Webster's method gives all three seats to A and none to B. The modified quota for A lies between 2.5 and 3.5.

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To show: More than 8313% of the country’s population must live in state A.

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Chapter 4 Solutions

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More than 8313% of the country’s population must live in state A.