#### Answer

Using Hamilton's method, each state is apportioned the following number of congressional seats.
State A is apportioned 7 seats.
State B is apportioned 13 seats.
State C is apportioned 27 seats.
State D is apportioned 33 seats.

#### Work Step by Step

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 fractional parts in their standard quotas until there are no more surplus seats.
State A's standard quota is 6.9
State A's lower quota is 6
State A's upper quota is 7
State B's standard quota is 13.3
State B's lower quota is 13
State B's upper quota is 14
State C's standard quota is 26.7
State C's lower quota is 26
State C's upper quota is 27
State D's standard quota is 33.1
State D's lower quota is 33
State D's upper quota is 34
Initially, each state is apportioned its lower quota.
State A is apportioned 6 seats.
State B is apportioned 13 seats.
State C is apportioned 26 seats.
State D is apportioned 33 seats.
We can find the total number of seats which have been apportioned.
total = 6 + 13 + 26 + 33 = 78 seats
Since there is a total of 80 congressional seats, there are two surplus seats. The first seat is given to state A because it has the largest fractional part (0.9) in its standard quota. The second seat is given to state C because it has the second largest fractional part (0.7) in its standard quota.
Using Hamilton's method, each state is apportioned the following number of seats.
State A is apportioned 6 + 1 = 7 seats.
State B is apportioned 13 seats.
State C is apportioned 26 + 1 = 27 seats.
State D is apportioned 33 seats.