Question

the student to faculty ratio at a small college is 17:3. the total of students and faculty is 740. how many faculty members are there at the college? how many students?

Answer 1

X - students
y - faculty members

The student to faculty ratio is 17:3.
x:y=17:3
$\frac{x}{y}=\frac{17}{3} \\ x=\frac{17}{3}y$

The number of students and faculty is 740.
$x+y=740 \\ x=\frac{17}{3}y \\ \Downarrow \\ \frac{17}{3}y+y=740 \ \ \ |\times 3 \\ 17y+3y=2220 \\ 20y=2220 \\ y=111 \\ \\ x=\frac{17}{3}y=\frac{17}{3} \times 111=\frac{1887}{3}=629$

There are 629 students and 111 faculty members at the college.

Answer 2

So students:faculty=17:3
total =740
we can assume that the units are the same so 17+3=20 so
740=20 units
74=2 units
37=1 unit

faculty=3 units
37 times 3=111
there are 111 faculty members