A community college has 3,000 students and 90 instructors. The college plans that enrollment will
Be 3,500 next year. How many new instructors should be hired if the college wants to keep the
Same student to instructor ratio?
A)77 instructors
B)15 instructors
C)105 instructors
D)13 instructors

Question

Quizplus · Accepted Answer

To maintain the same student to instructor ratio, we need to keep the ratio of students to instructors constant.

Current ratio: 
Number of students = 3,000 
Number of instructors = 90

Ratio of students to instructors = Number of students / Number of instructors 
= 3,000/90 
= 33.33 (approx.)

To maintain the same ratio with 3,500 students:

Number of students = 3,500 
Number of new instructors = x

Ratio of students to instructors = Number of students / Number of instructors 
33.33 = 3,500 / (90 + x)

Solving for x:

33.33(90+x) = 3,500 
3,000 + 33.33x = 3,500 
33.33x = 500 
x = 15

Therefore, the college should hire 15 new instructors. To maintain the same student to instructor ratio, the number of students per instructor should remain constant. Therefore, we can set up a proportion:

3,000 students / 90 instructors = 3,500 students / x instructors

Simplifying this equation, we get:

x = (90 * 3,500) / 3,000 = 105

This means that the college should have 105 instructors for 3,500 students. Since they currently have 90 instructors, they need to hire 15 new instructors. Therefore, the best choice is B) 15 instructors.

A Community College Has 3,000 Students and 90 Instructors