SOLUTION: four-sevenths of a school's faculty are women. four-fifths of the male faculty members are married, and nine of the male faculty are unmarried. how many faculty members are there?

Algebra ->  Proportions -> SOLUTION: four-sevenths of a school's faculty are women. four-fifths of the male faculty members are married, and nine of the male faculty are unmarried. how many faculty members are there?      Log On


   

Question 569360: four-sevenths of a school's faculty are women. four-fifths of the male faculty members are married, and nine of the male faculty are unmarried. how many faculty members are there?
Answer by IWork4Dessert(60) About Me  (Show Source):
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Let's work this from the end to the start. You know two things about the male faculty members, so begin with those. 4/5 of the men are married, and 9 of them are not. This means that 1/5 of the men are unmarried, so 9 is 1/5 of the total amount of men. Now you can set up a proportion:
1/5=9/x
Solve the proportion by cross-multiplying.
x=45
There are 45 men total. You know now that since 4/7 of the faculty are women, then 3/7 of them are men. So you have another proportion:
3/7=45/x
Cross-multiply again.
3x=315
Divide both sides by 3 to get the variable(letter) alone.
x=105
105 people are in the faculty total.