Anyone familiar with the The Hamilton method? And Apportion? PLEASE HELP!?

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cruz33

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The 37th pearl. Three friends have bought a bag guaranteedto contain 36 high-quality pearls for $14,900 at an auction.

Abe contributed $5900,
Beth’s contribution was $7600,
and Charles supplied the remaining $1400.

After taking the bag to your house, they pour the 36 pearlsfrom the bag onto the kitchen table.

(a) How many should each friend get if the Hamilton method is used to apportion thepearls according to the size of the contributions?

(b) Charles has noticed the bag isn’t empty! Another pearlcomes out, and you are asked to recalculate the apportionment.

(c) How do you explain the result to Charles?

http://www.ctl.ua.edu/math103/apportionment/appmeth.htm

Hamilton’s Method

Also known as the Method of Largest Remainders andsometimes as Vinton's Method.
Procedure:

  1. Calculate the Standard Divisor.
  2. Calculate each state’s Standard Quota.
  3. Initially assign each state its Lower Quota.
  4. If there are surplus seats, give them, one at a time, to states in descending order of the fractional parts of their Standard Quota.
 
Resolved!

cruz33 said:
The 37th pearl. Three friends have bought a bag guaranteedto contain 36 high-quality pearls for $14,900 at an auction.

Abe contributed $5900,
Beth’s contribution was $7600,
and Charles supplied the remaining $1400.

After taking the bag to your house, they pour the 36 pearlsfrom the bag onto the kitchen table.

(a) How many should each friend get if the Hamilton method is used to apportion thepearls according to the size of the contributions?

(b) Charles has noticed the bag isn’t empty! Another pearlcomes out, and you are asked to recalculate the apportionment.

(c) How do you explain the result to Charles?

http://www.ctl.ua.edu/math103/apportionment/appmeth.htm

Hamilton’s Method

Also known as the Method of Largest Remainders andsometimes as Vinton's Method.
Procedure:

  1. Calculate the Standard Divisor.
  2. Calculate each state’s Standard Quota.
  3. Initially assign each state its Lower Quota.
  4. If there are surplus seats, give them, one at a time, to states in descending order of the fractional parts of their Standard Quota.
Click to expand...
resolved!!!
 
That's a very nice explanation of the "Hamilton Method". Why have you not done any calculations? Abe contributed $5900 which is \(\displaystyle \frac{5900}{14900}= .3959...\) of the whole (that 14900 is the "standard divisor"). Beth contributed $7600 which is \(\displaystyle \frac{7600}{14900}= .5101\) of the whole. Charles contributed $1400 which is \(\displaystyle \frac{1400}{14900}= .0930\) of the whole. Dividing the 36 pearls in that proportion, .3959(36)= 14.2524, .5101(36)= 18.3636, and .0930(36)= 3.348, the problem being, of course, that those are not integers. So "Lower Quota" is "Abe, 14; Beth, 18; Charles, 3". That totals 14+ 18+ 3= 35 so there is one pearl left over. Since the largest fraction is ".3636", for Beth, we give her that left over pearl; Abe, 14, Beth, 19; Charles, 3. If there were a second left over pearl, there would be 37 pearls to begin with so multiply by 37 rather than 36:
Abe, .3959*37= 14.6483, Beth .5101*37= 18.8737, Charles, .0930*37= 3.441. The lower quota is still 14, 18, 3. Beth still has the largest fraction so gets a pearl. Abe now has the second largest fraction, .6438 so he gets the second pearl: Abe 15, Beth 19, Charles 3.

Notice that with 36 pearls, Charles had a larger "fraction" than Abe, but with 37, lower. You explain to Charles why he doesn't get the second pearl!
 
Last edited:
I resolved it already....

Why have you not done any calculations? You explain to Charles why he doesn't get the second pearl![/QUOTE]

Hi I already wrote under my own post "Resolved", did you not see it? After writing it here, I tried resolving it on my own, but left my post here just in case I got stuck and somebody was kind enough to help me. But, I did not get stuck (yay! for me) and this is why I came back and wrote under my post "resolved". Anyways, thank you very much for replying to my post, I really appreciate it!
 
Notice that the time tag on your second post was "7:53" and on mine "7:54". No, I didn't see your post! You posted while I was typing my response.
 
Like I said, thanks anyways! :)

HallsofIvy said:
Notice that the time tag on your second post was "7:53" and on mine "7:54". No, I didn't see your post! You posted while I was typing my response.
Click to expand...
Like I said, thanks anyways! :) Have a great day!
 
For future reference, if you have already done a problem and want someone to check your work- you will need to show your work. If you just ask for someone else to do the problem so that you can check it against your work, don't be surprized if others think you really just want someone to do the work for you!
 
Ok

HallsofIvy said:
For future reference, if you have already done a problem and want someone to check your work- you will need to show your work. If you just ask for someone else to do the problem so that you can check it against your work, don't be surprized if others think you really just want someone to do the work for you!
Click to expand...

ok!
 
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