i need help on math

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 14 tutors, determine how many tutors should be assigned to each subject using Jefferson's method.

Subject	Students Enrolled	Tutors to Assign
Math	355
English	205
Chemistry	115
Biology	85

What modified divisor did you use?

Answer 1

(355+205+115+85)/14=54.2

355/54.2→6.55, 6 tutors

205/54.2→3.78, 3 tutors

115/54.2→2.12, 2 tutors

85/54.2→1.57, 1 tutor

2 tutors surplus

Since the various number of students are multiples of 5, use 50 as a divisor.

355/50→7.1, 7 tutors

205/50→4.1, 4 tutors

115/50→2.3, 2 tutors

85/50→1.7, 1 tutor

0 surplus tutors.

Answer 2

355+205+115+85 = 760 students need tutors, and there are only 14.

1. Determine how many people each tutor should represent. Do this by dividing the total population of all the class by the total number of tutors. This answer is called the standard divisor.

760 / 14 = 54.2857

2. Divide each subject's population by the standard divisor to determine how many tutors it should have. Record this answer to several decimal places. This answer is called the quota.

355 / 54.2857 = 6.5394737

205 / 54.2857 = 3.7763158

115 / 54.2857 = 2.1184211

85 / 54.2857 = 1.5657895

3. Cut off all the decimal parts of all the quotas (but don’t forget what the decimals were). These are the lower quotas. Add up the remaining whole numbers. This answer will always be less than or equal to the total number of tutors.

355 / 54.2857 = 6.5394737 to 6

205 / 54.2857 = 3.7763158 to 3

115 / 54.2857 = 2.1184211 to 2

85 / 54.2857 = 1.5657895 to 1

6+3+2+1 = 12

4. If the total from Step 3 was less than the total number of tutors, reduce the divisor and recalculate the quota and allocation. Continue doing this until the total in Step 3 is equal to the total number of tutors. The divisor we end up using is called the modified divisor or adjusted divisor.

355 / 54 = 6.5740741 to 6

205 / 54 = 3.7962963 to 3

115 / 54 = 2.1296296 to 2

85 / 54 = 1.5740741 to 1

355 / 53 = 6.6981132 to 6

205 / 53 = 3.8679245 to 3

115 / 53 = 2.1698113 to 2

85 / 53 = 1.6037736 to 1

repeat for 52, no change

355 / 51 = 6.9607843 to 6

205 / 51 = 4.0196078 to 4

115 / 51 = 2.2549020 to 2

85 / 51 = 1.6666667 to 1

6+4+2+1 = 13, not 14 so keep going

355 / 50 = 7.1000000 to 7

205 / 50 = 4.1000000 to 4

115 / 50 = 2.3000000 to 2

85 / 50 = 1.7000000 to 1

7+4+2+1 = 14

The modified divisor or adjusted divisor is 50.

Source: Jefferson's Method

math.libretexts

Applied_Mathematics/

Math_in_Society_(Lippman)