## 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: $standard~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{19,600}{240}$ $standard~quota = 81.67$ Jefferson's method is an apportionment method that involves rounding each quota down to the nearest whole number. If each state is apportioned its lower quota, then the total number of apportioned seats is 13 + 41 + 62 + 81 which is 197 seats. To obtain a sum of 200 seats, we need to use a modified divisor that is slightly less than the standard divisor of 240. Let's choose a modified divisor of 238. Note that it may require a bit of trial-and-error to find a modified divisor that works. We can find the modified quota for each state. State A: $modified~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{3320}{238}$ $modified~quota = 13.95$ State B: $modified~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{10,060}{238}$ $modified~quota = 42.27$ State C: $modified~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{15,020}{238}$ $modified~quota = 63.11$ State D: $modified~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{19,600}{238}$ $modified~quota = 82.35$ Using Jefferson's method, the modified quota is rounded down to the nearest whole number. Each state is apportioned the following number of seats: State A is apportioned 13 seats. State B is apportioned 42 seats. State C is apportioned 63 seats. State D is apportioned 82 seats. Note that the total number of seats apportioned is 200, so using a modified divisor of 238 is acceptable.