A large community collage has professors and lecturers. the total number of faculty members is 136. the school reported that they had 6 professors for every 11 lecturers. how many professors does the community collage employ?

88

Step-by-step explanation:

Lets call L the number if lecturers and P the professors. As all of them together sum 136:

P + L = 136

Then, as for every 11 lecturers they have 6 professors, we know that:

6 P = 11 L

If we divide both sides of this equation by 6:

6P / 6 = 11L / 6

P = (11/6) L

So we have the equivalence of 1 Professor in Lecturers. If we replace this equation on our first equation:

P + L = 136

(11/6) L + L = 136 or what is the same:

(11/6) L + (6/6) L = 136

(11+6) / 6 L = 136

17/6 L = 136

If we multiply both sides by 6/17

(17/6) L * (6/17) = 136 * 6/17

L = 48

So, we replace the number of lecturers to find P:

P + L = 136

P = 136 - L

P = 136 - 48

P = 88

The college employs 88 professors