The large community college has 76 professors and 212 lecturers
Solution:
Given that,
Total number of faculty = 228
Let, the number of professors be p, then the number of lecturers will be 228 – p
They have 5 professors for every 14 lecturers.
Then, ratio of professors to lecturers is 5 : 14
Expressing the ratio as fractions, we get,
[tex]\rightarrow \frac{\text {number of professors}}{\text {number of lecturers}}=\frac{5}{14}[/tex]
Plug in the values of number of professors and lecturers
[tex]\rightarrow \frac{p}{288-p}=\frac{5}{14}[/tex]
[tex]\begin{array}{l}{\rightarrow 14 \times p=(288-p) \times 5} \\\\ {\rightarrow 14 p=1440-5 p} \\\\ {\rightarrow 14 p+5 p=1440} \\\\ {\rightarrow 19 p=1440} \\\\ {\rightarrow p=75.789 \approx 76}\end{array}[/tex]
So, community has 76 professors, then, it will have 288 – 76 = 212 lecturers.
