Question

4. 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 members who do not
have a PhD is 10 more than the number of female faculty members who have a PhD. If a third of the male
faculty members in the Department have a PhD, then what is the number of female faculty members in the
Department with a PhD?

Answer 1

Step-by-step explanation:

Let a = number of females with PhD, b = number of males with PhD, c = number of females without PhD, d = number of males without PhD

a+b=14

c+d=30

c-a=10

number of females without PhD are ten more than females with PhD

(44-(a+c)/3=14-a

a third of the male faculty have PhD

44-a-c=42-3a

44-c=42-2a

c-2a=2

c-a=10

a=8

b=6

Hence number of females with PhD is 8.