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?
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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.
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