Answer
Using Webster's method, 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.
Work Step by Step
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.
