Question

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?

Answer 1

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?

Answer 2

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

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.

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