## Thinking Mathematically (6th Edition)

We can find the total number of patients. total patients = 453 + 650 + 547 + 350 total patients = 2000 We can find the standard divisor. $standard~divisor = \frac{total ~patients}{number~of~ nurses}$ $standard~divisor = \frac{2000}{250}$ $standard~divisor = 8$ We can find each shift's standard quota. The standard quota of each shift is the number of patients during the shift divided by the standard divisor. Shift A: $standard ~quota = \frac{patients}{standard~divisor}$ $standard~quota = \frac{453}{8}$ $standard~quota = 56.63$ Shift B: $standard ~quota = \frac{patients}{standard~divisor}$ $standard~quota = \frac{650}{8}$ $standard~quota = 81.25$ Shift C: $standard ~quota = \frac{patients}{standard~divisor}$ $standard~quota = \frac{547}{8}$ $standard~quota = 68.38$ Shift D: $standard ~quota = \frac{patients}{standard~divisor}$ $standard~quota = \frac{350}{8}$ $standard~quota = 43.75$ Hamilton's method is an apportionment method that involves rounding each standard quota down to the nearest whole number. Surplus nurses are given, one at a time, to the shifts with the largest fractional parts in their standard quotas until there are no more surplus nurses. Initially, each shift is apportioned its lower quota. Shift A is apportioned 56 nurses. Shift B is apportioned 81 nurses. Shift C is apportioned 68 nurses. Shift D is apportioned 43 nurses. We can find the total number of nurses which have been apportioned. total = 56 + 81 + 68 + 43 = 248 nurses Since there is a total of 250 nurses available, there are two surplus nurses. The first nurse is given to Shift D because it has the largest fractional part (0.75) in its standard quota. The second nurse is given to Shift A because it has the second largest fractional part (0.63) in its standard quota. Using Hamilton's method, each shift is apportioned the following number of nurses: Shift A is apportioned 56 + 1 = 57 nurses. Shift B is apportioned 81 nurses. Shift C is apportioned 68 nurses. Shift D is apportioned 43 + 1 = 44 nurses.