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 21 tutors, determine how many tutors should be assigned to each subject using hamiltons method.
subject students enrolled tutors to assign
math 285
english 280
chemistry 120
biology 55
question help: video message instructor

Explanation:

Step1: Calculate the total number of students

$285 + 280+120 + 55=740$

Step2: Calculate the standard divisor

The standard divisor (SD) is the total number of students divided by the number of tutors. So, $SD=\frac{740}{21}\approx35.238$

Step3: Calculate the standard quota for each subject

For Math: $\text{Standard Quota}_\text{Math}=\frac{285}{35.238}\approx8.09$
For English: $\text{Standard Quota}_\text{English}=\frac{280}{35.238}\approx7.95$
For Chemistry: $\text{Standard Quota}_\text{Chemistry}=\frac{120}{35.238}\approx3.41$
For Biology: $\text{Standard Quota}_\text{Biology}=\frac{55}{35.238}\approx1.56$

Step4: Find the lower - quota for each subject

The lower - quota is the integer part of the standard quota.
For Math: $\lfloor8.09
floor = 8$
For English: $\lfloor7.95
floor = 7$
For Chemistry: $\lfloor3.41
floor = 3$
For Biology: $\lfloor1.56
floor = 1$
The sum of the lower - quotas is $8 + 7+3 + 1=19$

Step5: Allocate the remaining tutors

Since we need to assign 21 tutors and the sum of lower - quotas is 19, we have $21-19 = 2$ remaining tutors.
We assign the remaining tutors to the subjects with the largest fractional parts of their standard quotas.
The fractional part of Math's standard quota is $8.09 - 8=0.09$
The fractional part of English's standard quota is $7.95 - 7 = 0.95$
The fractional part of Chemistry's standard quota is $3.41 - 3=0.41$
The fractional part of Biology's standard quota is $1.56 - 1=0.56$
English and Biology have the largest fractional parts. So we add 1 tutor each to English and Biology.

Answer:

Math: 8
English: 8
Chemistry: 3
Biology: 2