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 16 tutors, determine how many tutors should be assigned to each subject using Jefferson's method.
\begin{tabular}{|l|l|l|}
\hline Subject & Students Enrolled & Tutors to Assign \\
\hline Math & 305 & \\
\hline English & 315 & \\
\hline Chemistry & 140 & \\
\hline Biology & 65 & \\
\hline
\end{tabular}
What modified divisor did you use?
Answer
The final allocation of tutors is: Math: 6 tutors, English: 7 tutors, Chemistry: 2 tutors, Biology: 1 tutor. The modified divisor used is 0.021. So, the final answer is \(\boxed{Math: 6, English: 7, Chemistry: 2, Biology: 1}\)
Step 1 ：Calculate the standard divisor (SD). The standard divisor is calculated by dividing the total number of items (in this case, tutors) by the total population (in this case, students). So, \(SD = \frac{Total \, tutors}{Total \, students} = \frac{16}{825} = 0.01939\) (rounded to 5 decimal places)
Step 2 ：Calculate the standard quotas (SQ). The standard quota for each subject is calculated by multiplying the number of students in that subject by the standard divisor. So, \(SQ_{Math} = 305 \times 0.01939 = 5.91\), \(SQ_{English} = 315 \times 0.01939 = 6.10\), \(SQ_{Chemistry} = 140 \times 0.01939 = 2.71\), and \(SQ_{Biology} = 65 \times 0.01939 = 1.26\) (all rounded to 2 decimal places)
Step 3 ：Apply Jefferson's method. In Jefferson's method, we lower the standard quotas to the nearest whole number to get the initial allocation. So, the initial allocation for Math is 5, for English is 6, for Chemistry is 2, and for Biology is 1
Step 4 ：If the total initial allocation is less than the total number of tutors, increase the divisor slightly and repeat step 3. If the total initial allocation is more than the total number of tutors, decrease the divisor slightly and repeat step 3. Continue this process until the total initial allocation equals the total number of tutors. In this case, the total initial allocation (14) is less than the total number of tutors (16), so we need to increase the divisor slightly. After several trials, we find that a divisor of 0.021 gives us an initial allocation that equals the total number of tutors
Step 5 ：The final allocation of tutors is: Math: 6 tutors, English: 7 tutors, Chemistry: 2 tutors, Biology: 1 tutor. The modified divisor used is 0.021. So, the final answer is \(\boxed{Math: 6, English: 7, Chemistry: 2, Biology: 1}\)
