Question

The student to faculty ratio at a small college is 17:3. The TOTAL number of students and faculty is 740. How many facutly members are there at the college? How many students?

a. There are 111 faculty members and 629 students at the college.
b. There are 5000 faculty members and 5000 students at the college.
c. There are 60 faculty members and 560 students at the college.
d. There are 150 faculty members and 700 students at the college.

Answer 1

By solving the system of equations derived from the student to faculty ratio 17:3 and the total number of 740, it has been determined that there are 111 faculty members and 629 students at the college.

Step-by-step explanation:

The student to faculty ratio at a small college is 17:3, and the total number of students and faculty is 740. To find the number of faculty and students, we set up the ratio as two equations that represent a system:

• 17x + 3x = 740
• x = number of units for each part of the ratio

Combining like terms gives us 20x = 740, so x = 740 / 20 = 37. Now, we just multiply this unit by each part of the ratio:

• Students: 17 × 37 = 629
• Faculty: 3 × 37 = 111

So, there are 111 faculty members and 629 students at the college, which corresponds to answer choice a.