#### Answer

Using Hamilton'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:
$standard~quota = \frac{population}{standard~divisor}$
$standard~quota = \frac{19,600}{240}$
$standard~quota = 81.67$
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.