 In this video, we provide the solution to question number 15 for practice exam 3 for math 1030, in which case we have to we have to apportion 20 seats among three states ABC using the Huntington Hill method. Now Huntington Hill is a divisor method, so we have to look for a modified divisor for the sake of simplicity on this exam of modified divisors given to you of 12.25. So we're going to divide each of the three states populations by the modified divisor 12.25, in which case we get the following 150 divided by 12.25 gives us 12.5714. 66 divided by 12.25 is 5.38776 and then finally 30 divided by 12.25 gives us 2.44898. So now with the Huntington Hill method, we round the quotas up or down based upon whether they're larger or smaller than the geometric mean. Now, the geometric mean does compare to the arithmetic mean that is the point five rule does come into effect. If your decimal place is point five or bigger than your geometric mean, which is always smaller than the arithmetic mean, you have to be bigger than that. So if your point five are bigger, you are going to round up when it comes to geometric rounding. So you're going to get a 13 right there, 12.5 rounds up to 13. On the other hand, if your decimal part, if your residue is point four or smaller, that will always guarantee that you round down. So as this one is 5.3, that'll round down to five. But then if your decimal part is point four, that's when you're in the danger zone for which you need to check the geometric mean to be certain particular because your number there too is really, really small. So the gap between the geometric mean and the arithmetic mean, it could be quite large. We have to make sure we don't fall. We have to make sure we fall where we are. We don't know at the moment. We have to compute the geometric mean. So the geometric mean, we're going to compute the square root of two times three. So notice our quota, our modified quota, its lower quota would be two, its upper quota is three. So that's the number we're looking there. Two times three gives us six and using a calculator, the square root of six turns out to be 2.4494. We can probably stop there. If you compare that, it's like 2.448. Whoa, if you round to three decimal places, they look the same there, but 2.4489. This is a number that's teeny, teeny, teeny bit smaller than the geometric mean. So we're going to round this one down so we get two seats right there. And notice that 13 plus five plus two adds up to be 20, which then gives us a correct apportionment of the seats using the Huntington Hill method.