OK, so since the ratio of students to faculty is 12:1, this implies there is 12 students for every 1 faculty member. As a result of this we can make a fraction out of it. So now we have:
12/1. This will be the fraction in which we use to find out how many students we have in comparison to any given number of faculty members.
So getting to the first question, we have 2 faculty members, which means we have to find the number of students in the numerator such that:
12/1=x/2
So we know that 12/1 is 12, so this implies that there are 24 students, since 24/2 is also 12.
Second question: So this time we are given the number of students, but with the ratio, we will be able to find the answer so this time we have:
12/1=120/x, and we know that the number we have to divide 120 by to get 12 is 10. So there are 10 faculty members.
If there are 100 faculty members, then:
12/1=x/100, which means that 100 divided by some number is equal to 12. When we solve for x, we get 1200. So there are 1200 students there.
So now our last question states that we have 5,400 students. So using this same ratio, we have:
12/1=5400/x
12x=5400
5400/12=450.
So there would be 450 faculty members.
Thank you for sending this question.
