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

So, the ration is 17:3, you know that. Therefore, the change from # of students to the 17 is the same change as # teachers to 3. Knowing this, you also know that the total # of people ihas the same change as the total ratio. So 17+3 = 20. 740/20 = 37. So the change is 37. 3x37= 111   17x37=629 
You can check to make sure this answer is correct by adding the two final numbers. 111+629 = 740.  (Some find it easier to see lined up really pretty)
17 -- 3   total 20
 x -- y   total 740 
 Or, if you are visual, look at the picture I drew: 

143 75 107 13 the answer