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 13 tutors, determine how many tutors should be assigned to each subject using jeffersons method.

subject	students enrolled	tutors to assign
english	263	3 x
chemistry	100	1 √
biology	90	1 √

what modified divisor did you use? 50 x
question help: 29%

Explanation:

Step1: Calculate total students

$343 + 263+100 + 90=796$

Step2: Try different modified divisors

Let's start by trying a modified divisor. We know that the sum of the initial quotients $\frac{343}{d}+\frac{263}{d}+\frac{100}{d}+\frac{90}{d}$ should be close to 13 when we round down the quotients.
If we try $d = 80$:

• For Math: $\lfloor\frac{343}{80}

floor=\lfloor4.2875
floor = 4$

• For English: $\lfloor\frac{263}{80}

floor=\lfloor3.2875
floor = 3$

• For Chemistry: $\lfloor\frac{100}{80}

floor=\lfloor1.25
floor = 1$

• For Biology: $\lfloor\frac{90}{80}

floor=\lfloor1.125
floor = 1$
The sum is $4 + 3+1 + 1=9
eq13$.
If we try $d = 60$:

• For Math: $\lfloor\frac{343}{60}

floor=\lfloor5.7167
floor = 5$

• For English: $\lfloor\frac{263}{60}

floor=\lfloor4.3833
floor = 4$

• For Chemistry: $\lfloor\frac{100}{60}

floor=\lfloor1.6667
floor = 1$

• For Biology: $\lfloor\frac{90}{60}

floor=\lfloor1.5
floor = 1$
The sum is $5 + 4+1 + 1 = 11
eq13$.
If we try $d = 55$:

• For Math: $\lfloor\frac{343}{55}

floor=\lfloor6.2364
floor = 6$

• For English: $\lfloor\frac{263}{55}

floor=\lfloor4.7818
floor = 4$

• For Chemistry: $\lfloor\frac{100}{55}

floor=\lfloor1.8182
floor = 1$

• For Biology: $\lfloor\frac{90}{55}

floor=\lfloor1.6364
floor = 1$
The sum is $6+4 + 1+1=12
eq13$.
If we try $d = 50$:

• For Math: $\lfloor\frac{343}{50}

floor=\lfloor6.86
floor = 6$

• For English: $\lfloor\frac{263}{50}

floor=\lfloor5.26
floor = 5$

• For Chemistry: $\lfloor\frac{100}{50}

floor=\lfloor2
floor = 2$

• For Biology: $\lfloor\frac{90}{50}

floor=\lfloor1.8
floor = 1$
The sum is $6 + 5+2+1=14
eq13$.
If we try $d = 52$:

• For Math: $\lfloor\frac{343}{52}

floor=\lfloor6.5962
floor = 6$

• For English: $\lfloor\frac{263}{52}

floor=\lfloor5.0577
floor = 5$

• For Chemistry: $\lfloor\frac{100}{52}

floor=\lfloor1.9231
floor = 1$

• For Biology: $\lfloor\frac{90}{52}

floor=\lfloor1.7308
floor = 1$
The sum is $6+5 + 1+1=13$.

Answer:

Math: 6 tutors, English: 5 tutors, Chemistry: 1 tutor, Biology: 1 tutor, Modified divisor: 52