Question

a large community college has professors and lecturers.The total number of faculty members is 228 the school reported that they have 5 members for every 14 lecturers how mant type of faculty member does the community college employ

Answer 1

To determine the number of professors and lecturers at the community college, we can use the information given in the problem.

1. Let the number of lecturers be \( L \) and the number of professors be \( P \).
2. We know the total number of faculty members is:
\[
P + L = 228
\]
3. We also know that there are 5 professors for every 14 lecturers, which can be expressed as:
\[
\frac{P}{L} = \frac{5}{14}
\]
This can be rewritten as:
\[
P = \frac{5}{14}L
\]

Now we have a system of equations:
1. \( P + L = 228 \)
2. \( P = \frac{5}{14}L \)

Next, we can substitute the expression for \( P \) from the second equation into the first equation:

\[
\frac{5}{14}L + L = 228
\]
Combining the terms, we can express \( L \) in terms of a single fraction:
\[
\frac{5}{14}L + \frac{14}{14}L = 228
\]
\[
\frac{19}{14}L = 228
\]

Now, multiply both sides by 14 to eliminate the fraction:
\[
19L = 228 \times 14
\]
Calculating the right side:
\[
19L = 3192
\]

Now divide both sides by 19:
\[
L = \frac{3192}{19} = 168
\]

Now that we have \( L \), we can substitute it back into the equation for \( P \):
\[
P + 168 = 228
\]
\[
P = 228 - 168 = 60
\]

So the community college employs:
- **Professors:** 60
- **Lecturers:** 168

In total, the community college employs **two types** of faculty members: professors and lecturers.