## Thinking Mathematically (6th Edition)

We can find the total patient load. total load = 1714 + 5460 + 2440 + 5386 = 15,000 We can find the standard divisor. $standard ~divisor = \frac{total ~patient~load}{doctors}$ $standard ~divisor = \frac{15,000}{150}$ $standard ~divisor = 100$ If we use the standard divisor and round each standard quota up to the nearest whole number, the sum of the apportioned doctors will be 18 + 55 + 25 + 54 which is 152 doctors. To obtain a sum of 150 doctors, we need to find a modified divisor that is slightly more than the standard divisor. Let's choose a modified divisor of 101.2. Note that it may take some trial-and-error to find a modified divisor that works. We can find the modified quota for each clinic. Clinic A: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{1714}{101.2}$ $modified~quota = 16.94$ Clinic B: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{5460}{101.2}$ $modified~quota = 53.95$ Clinic C: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{2440}{101.2}$ $modified~quota = 24.11$ Clinic D: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{5386}{101.2}$ $modified~quota = 53.22$ Using Adams's method, we need to apportion the doctors rounding up the modified quota to the nearest whole number. The doctors are apportioned to the clinics as follows: Clinic A is apportioned 17 doctors. Clinic B is apportioned 54 doctors. Clinic C is apportioned 25 doctors. Clinic D is apportioned 54 doctors. Note that the sum of the apportioned doctors is 150 doctors, so using 101.2 as a modified divisor is acceptable.