Answer to Question #121315 in Algebra for Neka

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

Let X1 be the number of women with a degree.

X10 -, without degree

Y1 number of men with a degree

Y10 - no degree

Then X1 + Y1 = 14

X10 + Y10 = 30

X10 -X1 + 10

Y10 = 2 * Y1

we have 4 equations with four unknowns.

substitute the last two equations into the second equation

X1 + 2 + Y1 = 20

we subtract the first from here, we get Y1 = 6

therefore X1 = 8