## 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: $standard~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{19,600}{240}$ $standard~quota = 81.67$ Webster's method is an apportionment method that involves rounding each quota to the nearest whole number. If we do this, then the total number of apportioned seats is 14 + 42 + 63 + 82, which is 201 seats. To obtain a sum of 200 seats, we need to use a modified divisor that is slightly more than the standard divisor of 240. Let's choose a modified divisor of 240.4. 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: $modified~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{3320}{240.4}$ $modified~quota = 13.81$ State B: $modified~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{10,060}{240.4}$ $modified~quota = 41.85$ State C: $modified~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{15,020}{240.4}$ $modified~quota = 62.48$ State D: $modified~quota = \frac{population}{modified~divisor}$ $modified~quota = \frac{19,600}{240.4}$ $modified~quota = 81.53$ Using Webster's method, the modified quota is rounded to the nearest whole number. Each state is apportioned the following number of seats: State A is apportioned 14 seats. State B is apportioned 42 seats. State C is apportioned 62 seats. State D is apportioned 82 seats. Note that the total number of seats apportioned is 200, so using a modified divisor of 240.4 is acceptable.