Answer
Using Webster's method, the officers are apportioned to the precincts as follows:
Precinct A is apportioned 28 officers.
Precinct B is apportioned 34 officers.
Precinct C is apportioned 53 officers.
Precinct D is apportioned 14 officers.
Precinct E is apportioned 22 officers.
Precinct F is apportioned 29 officers.
Work Step by Step
We can find the total number of crimes.
total crimes = 446 + 526 + 835 + 227 + 338 + 456
total crimes = 2828
We can find the standard divisor.
$standard ~divisor = \frac{total ~crimes}{officers}$
$standard ~divisor = \frac{2828}{180}$
$standard ~divisor = 15.71$
If we use the standard divisor and round each standard quota to the nearest whole number, the sum of the apportioned officers will be 179 officers. To obtain a sum of 180 officers, we need to find a modified divisor that is slightly less than the standard divisor.
Let's choose a modified divisor of 15.7. Note that it may take some trial-and-error to find a modified divisor that works. We can find the modified quota for each precinct.
Precinct A:
$modified~quota = \frac{crimes}{modified~divisor}$
$modified~quota = \frac{446}{15.7}$
$modified~quota = 28.41$
Precinct B:
$modified~quota = \frac{crimes}{modified~divisor}$
$modified~quota = \frac{526}{15.7}$
$modified~quota = 33.503$
Precinct C:
$modified~quota = \frac{crimes}{modified~divisor}$
$modified~quota = \frac{835}{15.7}$
$modified~quota = 53.18$
Precinct D:
$modified~quota = \frac{crimes}{modified~divisor}$
$modified~quota = \frac{227}{15.7}$
$modified~quota = 14.46$
Precinct E:
$modified~quota = \frac{crimes}{modified~divisor}$
$modified~quota = \frac{338}{15.7}$
$modified~quota = 21.53$
Precinct F:
$modified~quota = \frac{crimes}{modified~divisor}$
$modified~quota = \frac{456}{15.7}$
$modified~quota = 29.04$
Using Webster's method, we apportion the officers by rounding the modified quota to the nearest whole number. The officers are apportioned to the precincts as follows:
Precinct A is apportioned 28 officers.
Precinct B is apportioned 34 officers.
Precinct C is apportioned 53 officers.
Precinct D is apportioned 14 officers.
Precinct E is apportioned 22 officers.
Precinct F is apportioned 29 officers.
Note that the sum of the apportioned officers is 180, so using a modified divisor of 15.7 is acceptable.
