Question

a college offers tutoring in math, english, chemistry, and biology. the number of students enrolled in each subject is listed below. if the college can only afford to hire 18 tutors, determine how many tutors should be assigned to each subject using jeffersons method.
subject students enrolled tutors to assign
math 303
english 230
chemistry 155
biology 92
what modified divisor did you use?
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Explanation:

Step1: Calculate total students

The total number of students is $203 + 230+155 + 52=640$.

Step2: Initial divisor calculation

The initial divisor $d=\frac{\text{Total students}}{\text{Total tutors}}=\frac{640}{18}\approx35.56$.

Step3: Calculate initial quotas

For Math: $\text{Quota}_1=\frac{203}{35.56}\approx5.71$.
For English: $\text{Quota}_2=\frac{230}{35.56}\approx6.47$.
For Chemistry: $\text{Quota}_3=\frac{155}{35.56}\approx4.36$.
For Biology: $\text{Quota}_4=\frac{52}{35.56}\approx1.46$.

Step4: Take lower - quotas

Lower - quota for Math: $\lfloor5.71
floor = 5$.
Lower - quota for English: $\lfloor6.47
floor = 6$.
Lower - quota for Chemistry: $\lfloor4.36
floor = 4$.
Lower - quota for Biology: $\lfloor1.46
floor = 1$.
The sum of lower - quotas is $5 + 6+4 + 1=16$. Since we need 18 tutors, we need to adjust the divisor.

Step5: Adjust the divisor

We try a modified divisor. Let's try $d = 32$.
For Math: $\frac{203}{32}\approx6.34$, lower - quota $\lfloor6.34
floor = 6$.
For English: $\frac{230}{32}\approx7.19$, lower - quota $\lfloor7.19
floor = 7$.
For Chemistry: $\frac{155}{32}\approx4.84$, lower - quota $\lfloor4.84
floor = 4$.
For Biology: $\frac{52}{32}\approx1.63$, lower - quota $\lfloor1.63
floor = 1$.
The sum of these lower - quotas is $6 + 7+4 + 1=18$.

Answer:

Math: 6
English: 7
Chemistry: 4
Biology: 1
Modified divisor: 32