SOLUTION: The ratio of male to female employees in an office is 3:7. When 8 additional female employees are hired the ratio becomes 3:9. How many male employees does the office have?
Question 916510: The ratio of male to female employees in an office is 3:7. When 8 additional female employees are hired the ratio becomes 3:9. How many male employees does the office have? Answer by Theo(13342) (Show Source):
cross m/f = 3/7 to get:
7m = 3f
divide both sides of this equation by 3 to get:
7m/3 = f which is the same as f = 7m/3
cross multiply m/(f+8) = 3/9 to get:
3*(f+8) = 9m
simplify to get:
3f+24 = 9m
replace f with 7m/3 in 3f+24 = 9m to get:
3(7m/3) + 24 = 9m
simplify to get:
7m + 24 = 9m
subtract 7m from both sides of the equation to get:
24 = 2m
divide both sides of the equation by 2 to get:
12 = m which is the same as m = 12
in the equation m/f = 3/7, replace m with 12 to get:
12/f = 3/7
cross multiply to get 84 = 3f
divide both sides of the equation by 3 to get:
28=f which is the same as f = 28
you have m = 12 and f = 28
m/f = 3/7 becomes 12/28 = 3/7 which becomes 3/7 = 3/7 which confirms m = 12 and f = 28 is a good solution.
m/(f+8) = 3/9 becomes 12/(28+8) = 3/9 which becomes 12/36 = 3/9 which becomes 3/9 = 3/9 which also confirms m = 12 and f = 28 is a good solution.
