Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 13 - Voting and Apportionment - 13.3 Apportionment Method - Exercise Set 13.3: 5

Answer

Using Hamilton's method, each school is apportioned the following number of computers: Humanities is apportioned 30 computers. Social Science is apportioned 41 computers. Engineering is apportioned 53 computers. Business is apportioned 73 computers. Education is apportioned 103 computers.

Work Step by Step

We can find the total enrollment. total enrollment = 1050 + 1410 + 1830 + 2540 + 3580 total enrollment = 10,410 We can find the standard divisor. $standard~divisor = \frac{total ~enrollment}{number~of~ computers}$ $standard~divisor = \frac{10,410}{300}$ $standard~divisor = 34.7$ We can find each school's standard quota. The standard quota of each school is the school's enrollment divided by the standard divisor. Humanities: $standard ~quota = \frac{enrollment}{standard~divisor}$ $standard~quota = \frac{1050}{34.7}$ $standard~quota = 30.26$ Social Science: $standard ~quota = \frac{enrollment}{standard~divisor}$ $standard~quota = \frac{1410}{34.7}$ $standard~quota = 40.63$ Engineering: $standard ~quota = \frac{enrollment}{standard~divisor}$ $standard~quota = \frac{1830}{34.7}$ $standard~quota = 52.74$ Business: $standard ~quota = \frac{enrollment}{standard~divisor}$ $standard~quota = \frac{2540}{34.7}$ $standard~quota = 73.20$ Education: $standard ~quota = \frac{enrollment}{standard~divisor}$ $standard~quota = \frac{3580}{34.7}$ $standard~quota = 103.17$ Hamilton's method is an apportionment method that involves rounding each standard quota down to the nearest whole number. Surplus computers are given, one at a time, to the schools with the largest fractional parts in their standard quotas until there are no more surplus computers. Initially, each school is apportioned its lower quota. Humanities is apportioned 30 computers. Social Science is apportioned 40 computers. Engineering is apportioned 52 computers. Business is apportioned 73 computers. Education is apportioned 103 computers. We can find the total number of computers which have been apportioned. total = 30 + 40 + 52 + 73 + 103 = 298 computers Since there is a total of 300 computers, there are two surplus computers. The first computer is given to Engineering because it has the largest fractional part (0.74) in its standard quota. The second computer is given to Social Science because it has the second largest fractional part (0.63) in its standard quota. Using Hamilton's method, each school is apportioned the following number of computers: Humanities is apportioned 30 computers. Social Science is apportioned 40 + 1 = 41 computers. Engineering is apportioned 52 + 1 = 53 computers. Business is apportioned 73 computers. Education is apportioned 103 computers.
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