Division Fair Nathan Sullivan Within the Fair Division problem the reader is met with two problems on the sheet. The first of the two talks of three friends that go to a wine auction. They end up buying 20 bottles of wine all together. The first of the friends is named Jared; he has put in a total of $306. The second is named Michael who has put $207 toward their bottles of wine. The finale of the three is named Robert who has put in the most money with a total of $387. With this information the reader must now show who will get how many bottles of wine by how much they have paid. To do this the reader must first find out what the total cost of the wine was by adding all the amounts together, after doing this they will find that the total equals $900. And once they have found this the next step is to divided the total cost by how many bottles were purchased (20) this number will then be 45, showing that it cost was $45 per bottle. With this new information the reader can find out how many bottles each man will get by dividing how much he paid by $45. With this method the answers will come out with a decimal but because you can't split a bottle of wine the reader must subtract the decimals off of theses numbers. So with this Robert will get 8 bottles, Michael will get 4, and Jared will get 6. However this problem is not finished yet because now the reader must now take the subtracted decimal points and add them together (.6+. 8+. 6) once these numbers have been added up they will come to a solid 2 bottles over. left And because Robert and Jared put in the most money they should split the two bottles so they both get one. Meaning that in the end Jared has a total of 7 bottles of wine, Michael has a total of 4, and Robert has the most with 9 bottles.
The second problem works in the same way except that instead of men with wine is now women and DVD's. Also there is one other strange fact the problem never say's which woman paid what amount. This is all of the given information: Abby, Justi, and Megan go to take advantage of a DVD sale and that they buy a total of 40 DVD's. At this sale one of them pays $291.20, the other pays $145.60, and the last pays $83.20. As in the first problem the reader must first add up all of the amounts, which in this case add to a total of $520 for 40 DVD's. First the reader divides 520 by 40 getting the number 13, meaning that one DVD cost $13. Now the reader must divide the amounts that the women have spent by 13. This answer will again have a decimal point at the end of it that point will be subtracted to make the answers a whole number. This would mean that the woman that paid $291 would get 22 DVDs, and the woman that paid $83 would get 6, where as the woman that paid $145 would get 11 DVDs. After these numbers have been attained the reader must now add up all the decimal points (.2+. 4+. 4) which would add up to 1 whole DVD. And I believe that this should go to the woman that paid the most.
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