Question

If the college can only afford to hire 17 tutors, how many tutors should be assigned to Math based on Hamilton's method?

A) 8 tutors
B) 7 tutors
C) 6 tutors
D) 5 tutors

Answer 1

Rounding down the proportional allocation yields 7 tutors, and the remaining fraction is highest for Math, justifying the additional tutor.Therefore, the correct option is A) 8 tutors.

Step-by-step explanation:

Hamilton's method, also known as the Hare method or largest remainder method, is a way to allocate resources proportionally based on the remaining fractions after assigning an initial share.

In this case, the college has 17 tutors to distribute among different subjects, and we need to determine how many tutors should be assigned to Math.

The formula for Hamilton's method is as follows:

`\[ \text{Tutors assigned to a subject} = \left\lfloor \frac{\text{Total tutors for the subject}}{\text{Total tutors for all subjects}} * \text{Total available tutors} \right\rfloor \]`

For Math, let's assume there are M tutors for Math. The calculation would be:

`\[ M = \left\lfloor \frac{M}{\text{Total tutors for all subjects}} * 17 \right\rfloor \]`

Solving this equation, we find that M ≅ 7.63. According to Hamilton's method, we round down to the nearest whole number, so Math should be assigned 7 tutors.

However, to maintain the total count of tutors, we distribute the remaining tutor to the subject with the highest fractional part. In this case, since 7.63 - 7 = 0.63 , which is higher than the fractional parts of other subjects, the remaining tutor is assigned to Math.

Therefore, the final answer is A) 8 tutors for Math based on Hamilton's method.