Thinking Mathematically (6th Edition)

Published by Pearson

Chapter 13 - Voting and Apportionment - 13.3 Apportionment Method - Exercise Set 13.3 - Page 874: 6

Answer

Using Hamilton's method, each school is apportioned the following number of computers: Liberal Arts is apportioned 32 computers. Education is apportioned 36 computers. Business is apportioned 59 computers. Engineering is apportioned 81 computers. Sciences is apportioned 92 computers.

Work Step by Step

We can find the total enrollment. total enrollment = 1180 + 1290 + 2140 + 2930 + 3320 total enrollment = 10,860 We can find the standard divisor. $standard~divisor = \frac{total ~enrollment}{number~of~ computers}$ $standard~divisor = \frac{10,860}{300}$ $standard~divisor = 36.2$ We can find each school's standard quota. The standard quota of each school is the school's enrollment divided by the standard divisor. Liberal Arts: $standard ~quota = \frac{enrollment}{standard~divisor}$ $standard~quota = \frac{1180}{36.2}$ $standard~quota = 32.60$ Education: $standard ~quota = \frac{enrollment}{standard~divisor}$ $standard~quota = \frac{1290}{36.2}$ $standard~quota = 35.64$ Business: $standard ~quota = \frac{enrollment}{standard~divisor}$ $standard~quota = \frac{2140}{36.2}$ $standard~quota = 59.12$ Engineering: $standard ~quota = \frac{enrollment}{standard~divisor}$ $standard~quota = \frac{2930}{36.2}$ $standard~quota = 80.94$ Sciences: $standard ~quota = \frac{enrollment}{standard~divisor}$ $standard~quota = \frac{3320}{36.2}$ $standard~quota = 91.71$ 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. Liberal Arts is apportioned 32 computers. Education is apportioned 35 computers. Business is apportioned 59 computers. Engineering is apportioned 80 computers. Sciences is apportioned 91 computers. We can find the total number of computers which have been apportioned. total = 32 + 35 + 59 + 80 + 91 = 297 computers Since there is a total of 300 computers, there are three surplus computers. The first computer is given to Engineering because it has the largest fractional part (0.94) in its standard quota. The second computer is given to Sciences because it has the second largest fractional part (0.71) in its standard quota. The third computer is given to Education because it has the third largest fractional part (0.64) in its standard quota. Using Hamilton's method, each school is apportioned the following number of computers: Liberal Arts is apportioned 32 computers. Education is apportioned 35 + 1 = 36 computers. Business is apportioned 59 computers. Engineering is apportioned 80 + 1 = 81 computers. Sciences is apportioned 91 + 1 = 92 computers.

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