Answer:
The number of female faculty in the Department with a PhD is 8.
Step-by-step explanation:
There are 14 + 30 = 44 faculty members.
Of those, x are male and y are female.
Then
x + y = 44.
The number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD.
y = z + w
z is the number of females with PhD.
w is the number of females without PhD.
w = z + 10
If a third of the male faculty in the Department have a PhD
Now, we can write all variables as functions of z, which is the number of female faculty in the Department with PhD.
The objective is:
To find z from the first equation, that is:
To do this, we have to write x and y as functions of z.
Writing x and y as functions z.
And
In which
So
Replacing:
The number of female faculty in the Department with a PhD is 8.