At the Hardey Fitness Center, the management did a survey of their membership. The average age of the female members was 40 years old. The average age of the male members was 25 years old. The average age of the entire membership was 30 years old. What is the ratio of the female to male members? Express your answer as a common fraction.
Let f be the number of female members and m be the number of male members. Then the average age of the female members is 40f/(f+m) and the average age of the male members is 25m/(f+m).
Since the average age of the entire membership is 30, we have 40f/(f+m) + 25m/(f+m)=30, so 65f+25m=30f+30m, so 35f=5m, so f=5/7*m. Therefore, the ratio of female to male members is 5/7.