Question

The student to faculty ratio at Ventura College is 17:3. The total number of students and

faculty is 740. How many students and faculty are there?

Answer 1

To find the number of students and faculty at Ventura College with a ratio of 17:3 and a total of 740 people, we can solve a system of equations to get 629 students and 111 faculty members.

Step-by-step explanation:

The student to faculty ratio at Ventura College is 17:3. If the total number of students and faculty is 740, we can find out how many students and faculty there are by setting up a system of equations.

1. Let S represent the number of students and F represent the number of faculty.
2. The ratio gives us the equation 17F = 3S.
3. We also know that the total number of students and faculty is 740, so S + F = 740.
4. These two equations can be solved simultaneously.
5. From the ratio equation, we can express S in terms of F: S = (17/3)F.
6. Substituting S in the second equation: (17/3)F + F = 740.
7. Combining like terms, we get (20/3)F = 740.
8. Multiplying both sides by 3/20 yields F = 740 * (3/20).
9. That simplifies to F = 111 (faculty).
10. To find S, substitute F into the equation S = (17/3)F.
11. This results in S = (17/3)*111.
12. Calculating that gives us S = 629 (students).

Therefore, there are 629 students and 111 faculty members at Ventura College.