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.