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Direction: You must show ALL work to receive full credits. Any numerical answers without proper work shown will not receive full credit. You must show the equation set up for each of your calculation. Any work done on your calculator will not be counted as part of showing work. The provided table give the population of 15 states in 1790. If the House of Representatives has 105 members that are to be apportioned by the population of each state. Identify the basic terminologies and its values. How many representatives should each state get under the Hamilton's Method? 1. 2. State Virginia Massachusetts Pennsylvania North Carolina New York Maryland Connecticut South Carolina New Jersey New Hampshire Vermont Georgia Kentucky Rhode Island Delaware Population 630,560 475.327 432,879 353.523 331,589 278,514 236,841 206,236 179.570 141,822 70,835 68,705 68,446 55,540 Place your work and final answer on a separate sheet of paper. Be sure to clearly indicate and write out all your work to support your numerical values.

Explanation / Answer

a)Terminolgies

We will defined D which is the ratio between total population and total seats.

Here,total US population =Sum of all population of 15 states =P

total seats,T =105

D =P/T=3615920/105 = 34437.33

Now,the seats for each state =State population/D

2.Using Hamilton Method the total for each seat is shown below

Total US Population=630560+475327+432879+353253+331589+278514+236841+206236+179570+141822+85533+70835+68705+68446+55540=3615920

Finally rounding the each state quote the result of each state is shown in the last column.

State Population US Population Total Seats D State Quota Formula_State Quota Roundoff Virginia 630560 3615920 105 34437.33 18.310 630560/34437.33 18 Massachusetts 475327 3615920 105 34437.33 13.803 475327/34437.33 14 Pennsylvania 432879 3615920 105 34437.33 12.570 432879/34437.33 13 North Carolina 353523 3615920 105 34437.33 10.266 353523/34437.33 10 New York 331589 3615920 105 34437.33 9.629 331589/34437.33 10 Maryland 278514 3615920 105 34437.33 8.088 278514/34437.33 8 Connecicut 236841 3615920 105 34437.33 6.877 236841/34437.33 7 South Carolina 206236 3615920 105 34437.33 5.989 206236/34437.33 6 New Jersey 179570 3615920 105 34437.33 5.214 179570/34437.33 5 New Hampshire 141822 3615920 105 34437.33 4.118 141822/34437.33 4 Vermont 85533 3615920 105 34437.33 2.484 85533/34437.33 2 Georgia 70835 3615920 105 34437.33 2.057 70835/34437.33 2 Kentucky 68705 3615920 105 34437.33 1.995 68705/34437.33 2 Rhode Island 68446 3615920 105 34437.33 1.988 68446/34437.33 2 Delaware 55540 3615920 105 34437.33 1.613 55540/34437.33 2

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