In the Department of Natural Sciences, 14 faculty members have a PhD, and 30 faculty members do not have a PhD. In the Department, the number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD. If a third of the male faculty in the Department have a PhD, then what is the number of female faculty in the Department with a PhD?
Answers
The number of female faculty in the Department with a PhD is 8
Step-by-step explanation:
Total faculty members = 14 + 30 = 44
Thus, no. of female + male faculty = 44
Let the female faculty be x and male faculty be y
Then
x + y = 44 .............. (1)
If the no. of females having PhD is x'
Then, the no. of females not having Phd = x'+10
x'+x'+10 = x
or, 2x'+10=x
If the no. of males having PhD is y'
Then
According to the question
y' = y/3
or, y = 3y'
Therefore, from (1)
2x'+10+3y'=44
or, 2x' + 3y' = 34 ............... (2)
Total faculty members having PhD = 14
Thus
x' + y' = 14 ............... (3)
Multiplying (3) by 2 and subtracting it from eq (2)
We get
y' = 6
Thus, from (3)
x' = 8
Therefore, the number of female faculty in the Department with a PhD is 8
Hope this answer is helpful.
Know More:
Similar question:
https://brainly.in/question/18220619