Question
What is the number of new instructors a community college should hire to maintain a consistent student-to-instructor ratio if enrollment increases from 3,000 to 3,500 students, given that the current ratio is 33.33 students per instructor?
Answers
GPT-4o mini
To determine how many new instructors a community college should hire to maintain a consistent student-to-instructor ratio given the new enrollment, we can follow these steps:
1. **Calculate the current number of instructors**:
The current ratio is 33.33 students per instructor. Therefore, we can calculate the current number of instructors based on the current enrollment of 3,000 students.
\[
\text{Current number of instructors} = \frac{\text{Current enrollment}}{\text{Current student-to-instructor ratio}} = \frac{3000}{33.33} \approx 90
\]
2. **Calculate the required number of instructors for the new enrollment**:
With the new enrollment increasing to 3,500 students, we need to find out how many instructors are required to maintain the same ratio.
\[
\text{Required number of instructors} = \frac{\text{New enrollment}}{\text{Current student-to-instructor ratio}} = \frac{3500}{33.33} \approx 105
\]
3. **Determine the number of new instructors needed**:
Finally, we can find out how many additional instructors need to be hired by subtracting the current number of instructors from the required number of instructors.
\[
\text{New instructors needed} = \text{Required number of instructors} - \text{Current number of instructors} = 105 - 90 = 15
\]
Thus, the community college needs to hire **15 new instructors** to maintain the same student-to-instructor ratio as enrollment increases from 3,000 to 3,500 students.
1. **Calculate the current number of instructors**:
The current ratio is 33.33 students per instructor. Therefore, we can calculate the current number of instructors based on the current enrollment of 3,000 students.
\[
\text{Current number of instructors} = \frac{\text{Current enrollment}}{\text{Current student-to-instructor ratio}} = \frac{3000}{33.33} \approx 90
\]
2. **Calculate the required number of instructors for the new enrollment**:
With the new enrollment increasing to 3,500 students, we need to find out how many instructors are required to maintain the same ratio.
\[
\text{Required number of instructors} = \frac{\text{New enrollment}}{\text{Current student-to-instructor ratio}} = \frac{3500}{33.33} \approx 105
\]
3. **Determine the number of new instructors needed**:
Finally, we can find out how many additional instructors need to be hired by subtracting the current number of instructors from the required number of instructors.
\[
\text{New instructors needed} = \text{Required number of instructors} - \text{Current number of instructors} = 105 - 90 = 15
\]
Thus, the community college needs to hire **15 new instructors** to maintain the same student-to-instructor ratio as enrollment increases from 3,000 to 3,500 students.