A large community college has professors and lecturers. The total number of faculty is 228. The school reported that they have 5 professors for every 14 lecturers. how many of each type of each employee does the community college employ? ​

The large community college has 76 professors and 212 lecturersSolution:Given that,Total number of faculty = 228Let, the number of professors be p, then the number of lecturers will be 228 – pThey have 5 professors for every 14 lecturers. Then, ratio of professors to lecturers is 5 : 14Expressing 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.