Question

a college offers tutoring in math, english, chemistry, and biology. the number of students enrolled in each subject is listed below. the college can only afford to hire 18 tutors. use websters method to determine the initial allocations with the standard divisor, then finish the apportionment to determine how many tutors should be assigned to each subject.

subject	students enrolled	initial allocation	tutors to assign
english	235
chemistry	160
biology	65

what modified divisor did you use for the final apportionment?

Explanation:

Step1: Calculate total students

$300 + 235+160 + 65=760$

Step2: Calculate standard divisor

Standard divisor $SD=\frac{760}{18}\approx42.22$

Step3: Calculate initial allocations

For Math: $\frac{300}{42.22}\approx7.11$; initial allocation is 7
For English: $\frac{235}{42.22}\approx5.57$; initial allocation is 5
For Chemistry: $\frac{160}{42.22}\approx3.79$; initial allocation is 3
For Biology: $\frac{65}{42.22}\approx1.54$; initial allocation is 1
Sum of initial allocations $=7 + 5+3 + 1=16$
Since we need to assign 18 tutors, we use a modified divisor.
Let's try a modified divisor $MD = 40$

Step4: Calculate final allocations with modified divisor

For Math: $\frac{300}{40}=7.5$; round up to 8
For English: $\frac{235}{40}=5.875$; round up to 6
For Chemistry: $\frac{160}{40}=4$
For Biology: $\frac{65}{40}=1.625$; round up to 2
Sum of final allocations $=8 + 6+4 + 2=20$ (too high)
Let's try $MD = 45$
For Math: $\frac{300}{45}\approx6.67$; round up to 7
For English: $\frac{235}{45}\approx5.22$; round up to 5
For Chemistry: $\frac{160}{45}\approx3.56$; round up to 4
For Biology: $\frac{65}{45}\approx1.44$; round up to 2
Sum of final allocations $=7 + 5+4 + 2=18$

Answer:

Subject	Students Enrolled	Initial Allocation	Tutors to Assign
English	235	5	5
Chemistry	160	3	4
Biology	65	1	2

Modified divisor used for final apportionment: 45