#### Answer

Using Adams's method, 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.

#### Work Step by Step

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.