## Thinking Mathematically (6th Edition)

We can find the total population. total population = 3320 + 10,060 + 15,020 + 19,600 total population = 48,000 We can find the standard divisor. $standard~divisor = \frac{total~population}{number~of~ seats}$ $standard~divisor = \frac{48,000}{200}$ $standard~divisor = 240$ The standard divisor is 240. We can find the standard quota for each state. State A: $standard~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{3320}{240}$ $standard~quota = 13.83$ State B: $standard~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{10,060}{240}$ $standard~quota = 41.92$ State C: $standard~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{15,020}{240}$ $standard~quota = 62.58$ State D: $standard~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{19,600}{240}$ $standard~quota = 81.67$ Hamilton's method is an apportionment method that involves rounding each standard quota down to the nearest whole number. Surplus seats are given, one at a time, to the states with the largest decimal parts in their standard quotas until there are no more surplus seats. Initially, each state is apportioned its lower quota. State A is apportioned 13 seats. State B is apportioned 41 seats. State C is apportioned 62 seats. State D is apportioned 81 seats. The total number of seats which have been apportioned is 13 + 41 + 62 + 81, which is 197 seats Since there is a total of 200 seats, there are three surplus seats. The first seat is given to State B because it has the largest decimal part (0.92) in its standard quota. The second seat is given to State A because it has the second largest decimal part (0.83) in its standard quota. The third seat is given to State D because it has the third largest decimal part (0.67) in its standard quota. Using Hamilton's method, each state is apportioned the following number of seats: State A is apportioned 13 + 1 = 14 seats. State B is apportioned 41 + 1 = 42 seats. State C is apportioned 62 seats. State D is apportioned 81 + 1 = 82 seats.