On a certain college faculity, 4/7 of the professors are male, and the ratio of the professors older than 50 to the professors less than or equal to 50 years is 2:5. if 1/5 of the male professors are older than 50 years, what fraction of the female professors are less than or equal to 50 years ?
Solveit
Guest
Why NOT use concrete numbers for ALL professors!
Let us take the total numbers of professors to be=700
4/7 X 700=400 male professors
3/7 X 700=300 Female professors.
But we have a ratio of 2:5- being those >50 years of age to those <= 50 years of age. Therefore,
2/(2+5) X 700=200 male and female professors > 50 years of age, and similarly,
5/(2+5) X 700=500 male and female professors <=50 years of age. But 1/5 of male professors are older than 50 years, therefore,
1/5 X 400=80 male professors older than 50, and it follows that:
200 - 80 =120 female profeesors older than 50. Hence we have:
400 - 80 =320 male professors less than 50, and,
300 - 120=180 female professors less than 50. Therefore, the percentage of female professors <= 50 years, out of the total number of female professors is:
180/300=60% or 3/5. But, as a percentage of the total faculty of 700, then we have:
180/700=~25.71% or 9/35.
