 In this video, we provide the solution to question number 12 for practice exam number three for math 1030 In which case we have an apportionment problem Or we have six states for which we need to apportion 200 seats amongst those six states and we're gonna do that using Hamilton's method. So some things that I do need to compute I need to figure out what the total population that's not provided to me But if I take these numbers right here and add them all together, you're gonna get the total population Which is gonna be 100 but be aware this might have been somewhat obvious If you're like, oh, these are just the population percentages So the percentages should add up to you a hundred percent that makes sense But regardless we do know what the total population is Using the total population we can now compute the standard divisor which is critical for Hamilton's method So we're gonna take the total population, which is a hundred percent and we then divide it by the number of seats Which is 200 Right that was listed up here. And so that's gonna give us a standard divisor of one half or 0.5 if you prefer there and so using that standard divisor we're gonna compute all of the standard quotas So I'm gonna take for example 11.37 and I'm gonna divide it by 0.5 or if you want to think about your times in it by two so dividing by one half is the same thing as times you by two So you take 11.37 times it by two you're gonna get 22.74 I'm just gonna do two decimal places here then the next one eight point zero seven if you times it by two You get sixteen point one four Thirty eight point six two times it by two you get seventy seven point two four fourteen point nine eight if you times that by two you're gonna get twenty nine point nine six ten point four two times two gives you twenty point eight four and then lastly sixteen point five four if you times that by two you're gonna get thirty three point zero eight and So then with this Hamilton's method gives everyone their lower quota So you're gonna give state a 22 seats state b gets 16 state Charlie gets 77 state Delta gets 29 state Echo gets 20 and state is Foxtrot there. It's gonna get 33, but then look at how many we have right there So if you take 22 plus 16 plus 77 plus 29 plus 20 plus 33 That adds up to be a hundred and ninety seven which is three short So we have a surplus of three So we need to figure out who's the most deserving amongst them So looking at the residues the biggest residue would be point nine six So we're gonna bump state D up to 30 seats Next I'm looking the next biggest residue would be point eight four So e is gonna get upgraded to twenty one and then finally the next biggest residue is gonna be point seven four for state a So we're gonna give the last remaining seats to state a giving twenty three So the correct apportionment using Hamilton's method would be twenty three sixteen seventy seven thirty Twenty one and thirty three for states a b c d e f respectively